text:
Virginia Motor Speedway | Virginia Motor Speedway Releases 2015 Schedule
Jamaica, VA – The tentative 2015 schedule for Bill Sawyer's Virginia Motor Speedway has been released and includes 12 weeks of Virginia Army National Guard Dirt Series action, three special events and two mud bogs.
The track's always competitive weekly divisions begin their race for the division Championships and the Virginia Army National Guard Dirt Series Championship on Saturday April 18th and end with the final point's race of the season on Saturday September 5th.
This year's division line-up will once again include the Victory Lap Late Models, Aaron's Pro Late Models, Truckin Thunder Sportsman, Budweiser Modifieds and the Collision One Limited Stock Cars.
Opening up the 2015 season will be the Aaron's King of the Commonwealth sanctioned by the very popular Ultimate Super Late Model Series. The one day $20,000 event is expected to bring some of the nationals top super late model drivers back to the Commonwealth of Virginia for what will be one of the best races of the year. The Ultimate Super Late Model Series will then return on Saturday May 16th as they sanction the 37th Annual USA 100. For the first time the speedway will host two, $3000 to win Fastrak Pro Late Model "National Bonus Race" events in conjunction with both super late model events, making both events a late model fans dream.
After producing one of the best races in the track's history the Fastrak World Championship will return to the 2015 schedule. The "Super Bowl" of Pro Late Model racing is scheduled for September 18 – 19, 2015. The event will feature two, $3000 to win events on Friday, September 18th and the $15,000 to win finale on Saturday, September 19th that will crown the Fastrak Pro Late Model World Champion. More details about the Fastrak World Championship will be released in the very near future.
Along with the weekly racing action and the special events the speedway will also host two mud bogs at its state of the art mud bog facility that will be celebrating its eleventh year of racing. On Saturday June 20th "The Pit at VMS" will host the 7th Annual Down and Dirty Mud Mayhem and on Saturday October 10th the 11th Annual Down and Dirty Run-A-Muck Mud Bog and Mud Sling presented by James River Equipment and the Virginia Army National Guard.
To see the entire 2015 schedule in its entirety visit the Speedway's website at www.vamotorspeedway.com. The 2015 schedule is tentative and subject to change.
The speedway has begun to accepting registrations with the top twenty in each class having their number saved until February 15th when all numbers will become first come first served. Competitors will Competitors can obtain a 2015 registration form by going to the tracks website or by calling the speedway Monday through Friday 10am through 3pm at (804) 758-1867.
Bill Sawyer's Virginia Motor Speedway is a 1/2-mile, dirt oval. The track is located on U.S. Route 17, eight miles north of Saluda, VA and 25 miles south of Tappahannock, VA in Jamaica, VA. The speedway is just a short drive from Richmond, Fredericksburg, Southern Maryland and the Hampton Roads area.
To learn more about Bill Sawyer's Virginia Motor Speedway and its 2015 schedule of events, fans may call the Speedway office at (804) 758-1VMS or visit the track's web site at www.vamotorspeedway.com.


text:
Crooks lift plants, drop toilet
by David Taber • October 19, 2007 • 0 Comments
DAVID TABER
Since the Gazette published its exposé on local plant thievery in August, two more victims have come forward, one reporting the replacement of his shrubs with a broken toilet.
The other, Lisa Ganak, a professional floral designer, told the Gazette three large terra cotta pots filled with ivy, geraniums and bear grass, which she installed outside of El Oriental de Cuba restaurant in June, did not last a week.
The pots, ranging in size from one to three feet deep, were weighted with bricks and buried in two or three inches of mulch behind a white picket fence under a tree on Centre Street.
Noting the thieves did not disturb the mulch when they took the planters, Ganak speculated they lifted the 50-pound pots straight out of the ground.
"They must have been bodybuilders," she said.
Ganak was hired by El Oriental De Cuba owner Nobel Garcia to install the planters. The materials cost about $200, but she did not charge Garcia for her labor, she said.
She had been planning to use the El Oriental de Cuba installation as a calling card to try to attract business from other Centre Street storeowners, she said, but now has no plans to solicit their business.
"The message was clear: why do it?" Ganak said.
Ganak said she did not report the incident to the police.
Mark Angney also called into the Gazette, reporting the theft of a number of coniferous shrubs in May from the front yard of a house he owns that was under construction at 51 Green St.
The two-foot-high plants were dug out with shovels. "We are not just talking about snipping irises," Angney said.
Angney said he considered "setting up on the porch with a shotgun at 2 a.m.," but settled on posting a sign on the fence that read, "Stop pilfering my plants."
The strategy did not have the desired effect.
When he checked in the morning, thieves had stolen the sign, Angney said, "And there was a used toilet in the backyard."
Both calls came in shortly after Boston Globe presidential campaign reporter and Paul Gore Street resident Scott Helman published a personal narrative in the Boston Globe Magazine about flora getting nicked from his garden.
The subject came up again in early September when Helman hosted an online chat about the presidential race, the transcript of which was published on Boston.com. After someone else asked him how his flowers were, an individual with the screen name Cait wrote, "I had my flowers stolen off my front porch this spring too!"
To which Helman replied, "Really? I feel your pain. Where do you live?"
The conversation briefly turned to Mitt Romney's presidential prospects before Cait wrote that she lives in "a quiet neighborhood in Cambridge. It was quite a shocking affair."
"That is shocking. I live in Jamaica Plain, where others have been victims," Helman replied.
← Police park phone use unclear
BUG garden giveaway plans revealed this week →

redpajama_set_name: RedPajamaCommonCrawl


TTi Winter Camp December 18th-21st 2017 Closes Out Historic Year!
TTi are pleased to share the schedule for the upcoming December Camps for the Development Center and TTi.
"The Camps are included in our membership and are an integral part of development as we see the players in larger setting" said Sporting Director, lee Cullip "we are able to film the players and then share that with them post camp" Cullip concluded.
Molly Vega, Memorial Hermann Nutritionist will be giving a workshop to help fuel you for success in soccer. In addition to the Nutrition, we will be having a College Workshop working around the title "10 Things You Can do Now" conducted by our College Process Manager Matt Evans.
he camp runs 18th-22nd December 4-8pm at Regis School and is open to all members and we encourage them to bring a friend (Please just notify us you are)!
The camp is on Teamsnap and you can attend all the sessions or whatever you can make!


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\section{Introduction}

It is natural to ask what M(atrix) theory \cite{BFSS} has to say about
the physics of Schwarzschild black holes.  Several groups have
investigated this subject
\cite{BFKS,KlebanovSusskind,Halyo,HorowitzMartinec,Li,DMRR,BFKS2,TsLi,BFK,OhtaZhou,LiMartinec,Lowe}.
By modeling the black hole as a Boltzmann gas of 0-branes, several key
properties such as the entropy -- mass relationship and the Hawking
temperature have been derived, up to numerical coefficients of order
unity.

But the defining property of a black hole in classical gravity is the
existence of an event horizon.  In this paper we address the question
of how a horizon manifests itself in M(atrix) theory.  One's first
thought -- that the size of the horizon is given by the range of
eigenvalues of the matrices ${\bf X}_i$ -- cannot be correct, since
this range is expected to diverge in the large $N$ limit for all
states in M(atrix) theory.

In a scattering experiment the horizon area of a black hole can be
measured from its absorption cross section.  In the context of
M(atrix) theory this reflects the fact that a probe 0-brane should be
absorbed by the black hole once it crosses the horizon.

For Schwarzschild black holes in M(atrix) theory our proposal is that
the mechanism responsible for this absorption is a tachyon
instability: the probe 0-brane sees the horizon as a critical radius,
at which strings stretched between the probe and the black hole become
tachyonic.\footnote{A horizon is a global property of spacetime, which
cannot be detected by a local probe.  More precisely our proposal is
to associate the tachyon radius with a closed trapped surface, which
we shall loosely refer to as a horizon.}  This provides a precise
prescription for identifying the horizon in M(atrix) theory.

At a qualitative level, one can see that a state in gauge theory that
gives rise to such a tachyon region will have the features expected of
a black hole.  Suppose a probe enters the tachyon region.  Then the
tachyons will start to condense, so the probe will be captured with
very high probability.  Moreover, the tachyonic modes couple to all
the other degrees of freedom which make up the initial state, and the
energy released as the tachyon condenses is available to be
redistributed among all these degrees of freedom.  Thus within the
gauge theory we see that infalling matter gets absorbed and quickly
thermalized when it enters a region with a tachyon instability.  This
is all directly analogous to the behavior expected of matter falling
into a black hole.

Although our treatment will focus on 11-dimensional Schwarzschild
black holes, we expect the discussion of tachyon instability to apply
more generally to the horizon of non-extremal D-brane black holes, as
well as to non-extremal black holes in the context of anti de Sitter
space \cite{Maldacena}.

Extremal black holes must behave somewhat differently, however.  A
supersymmetric probe of an extremal black hole should still be
absorbed when it reaches the horizon, but the mechanism cannot be a
tachyon instability.  In section 3 we will give a brief discussion of
string pair creation as a possible mechanism in the extremal case.

An outline of this paper is as follows.  In section 2 we review some
facts about Schwarzschild black holes in M(atrix) theory and
absorption mechanisms in D-brane scattering.  In section 3 we argue
that a tachyon instability, if present, would have the features
expected of a Schwarzschild horizon in M(atrix) theory.  In section 4
we study the tachyon instability for several explicit M(atrix)
configurations.  Although we cannot directly study black hole states,
the examples we consider are sufficient to show that tachyons are
indeed present in M(atrix) theory, in regions which can plausibly be
associated with Schwarzschild horizons.  Section 5 contains some
conclusions.

\section{Preliminaries}

We review some relevant results concerning Schwarzschild black holes
in M(atrix) theory and absorption mechanisms in D-brane scattering.

\subsection{Schwarzschild black holes in M(atrix) theory}

The most general object in M(atrix) theory is a collection of 0-branes
with some strings stretching between them. The only truly stable
states are the gravitons, but a black hole can be thought of as a long
lived quasi-stable state. A Schwarzschild black hole has negative heat
capacity, unlike any state in SYM.  But in terms of light cone
variables a black hole actually has a positive heat capacity if the
number of non-compact dimensions is six or larger
\cite{KlebanovSusskind}.  This makes it possible to be described using
SYM.

Another feature of gravity that is relevant for black holes is that
one can't put an arbitrary amount of energy in a bounded region.  The
upper limit for a given region is the black hole mass with the horizon
area chosen appropriately.  In M(atrix) theory we can see a similar
effect. Fix the size of the matrices at $N \times N$, and choose some
volume with typical length $L$. We want to see if there is a limit on
the SYM energy, with the restriction that the object is contained
within the designated volume. This is easy to see at the classical
level of the SYM. For the moment let us define the size to be at most
the volume occupied by the eigenvalues of the matrices (which are not
necessarily simultaneously diagonalizable).  Now take nine diagonal
matrices with some distribution of eigenvalues $-L < \lambda <
L$. This state has zero energy. The most general configuration with
these eigenvalues can be obtained by acting with different unitary
matrices on each of the original nine matrices. As the magnitude of
each entry of a unitary matrix is smaller than 1, there is a limit on
the entries of the resulting nine matrices. Then it is clear that the
energy $\sim {\rm Tr} [{\bf X}_i, {\bf X}_j]^2$ is bounded.

Currently the best understood model for Schwarzschild black holes is
at the so-called BFKS point, that is when $N \sim S$ \cite{BFKS}. At
this point the temperature of the SYM is so low that quantum
fluctuations are of the same order as thermal fluctuations. To go
beyond this point, to $N \gg S$, requires a fully quantum mechanical
treatment of the system.  Following \cite{BFKS}, one can model black
holes with entropy $\sim N$ as follows.  The basic ingredient is a
state that has some expectation value for the matrices, $B_i = <{\bf
X}_i>$ (this is referred to as the background).  The SYM energy of
this state is identified with the light-cone energy of the black hole,
and the volume of the state is the volume of the black hole (we will
come back to what we mean by volume of the state). The background and
its fluctuations (which are modeled as a gas of N particles)
contribute to the entropy and energy of the state. In fact most papers
deal only with the thermodynamics of these fluctuations.

For the entropy to come out correctly it is crucial that the
statistics of the fluctuations be that of distinguishable particles.
This issue is somewhat subtle.  If all the background matrices commute
(so that they can be simultaneously diagonalized) then there is a
residual gauge symmetry that permutes the diagonal elements, which
makes the statistics that of identical particles. In this case the
entropy is very small.  To see this take a gas of free identical
particles in $d$ dimensions.  The assumed kinematics is that each
particle has momentum $p_\perp \sim 1/R_S$ set by the uncertainty
principle and mass $m=1/R$, where $R_S$ is the Schwarzschild radius
and $R$ is the radius of the null circle.  The volume of the gas is
$V=\left(R_{S}\right)^{d}=N$ at the BFKS point. The energy of the gas
is then $E \sim N R / R_{S}^{2}$. For a gas of $N$ distinguishable
particles in $d$ space dimensions the entropy is
\begin{equation}
S=N\log \left[V\left(\frac{4\pi m E}{d N}\right)^{d/2}\right]
+\frac{d N}{2}
\end{equation}
This entropy is indeed $\sim N$. If the particles are identical then
the volume $V$ would be replaced with $V/N$ and there would be very
little entropy.

If the background matrices do not commute (which means that there is a
coherent state of strings stretched between different 0-branes) then
we no longer have the residual gauge symmetry discussed above and thus
do not have identical particles. The factor $1/N$ will not appear and
the entropy will be order $N$.  But the parameter which breaks the
statistics symmetry is continuous, and it is not entirely clear at
what value the effective statistics actually changes. For instance, if
the energy in the fluctuations is much larger than the energy of the
background then it is not clear why the above analysis should apply.

Another issue is how to measure the size of a state. Clearly it cannot
simply be the volume occupied by the 0-branes (although this will
provide an upper bound) since, according to the holographic principle,
this is expected to grow with $N$ even for a graviton \cite{BFKS}. The
most physical measure of the size of a state is through scattering
experiments.  For a black hole, in particular, it is natural to use
the absorption cross-section as a definition of the horizon size.  So
before applying this definition to M(atrix) black holes we briefly
review absorption mechanisms in D-brane scattering.

\subsection{Absorption in D-brane scattering}

In D-brane scattering there are two mechanisms which contribute to the
imaginary part of the phase shift and lead to absorption.

The first mechanism is string creation.  When two D-branes have
non-zero relative velocity, there is an amplitude to pair create two
oppositely-oriented open strings stretched between them.  Since
velocity is T-dual to an electric field on the D-brane worldvolume,
and open strings carry electric charge, this is dual to the phenomenon of
pair production in an electric field \cite{BachasPorrati}.

In the scattering amplitude, string creation arises as follows.  The
one-loop eikonal phase shift for D0 -- D0 scattering has the form ($b$
is the impact parameter and $v$ is the relative velocity)
\cite{Bachas}
\begin{equation}
\delta(b,v) \sim \int_0^\infty \frac{ds}{s} e^{-b^2s/2 \pi \alpha'}
\frac{f(s,v)}{\sin sv}
\label{del}
\end{equation}
At $sv=n \pi$ the integrand has poles which contribute an imaginary
part to the phase shift.  The outgoing wavefunction of the scattered
0-brane is multiplied by $e^{i\delta}$.  Significant string creation
is possible only for $b < \sqrt{v \alpha'}$, since for large $b$ the
imaginary part is exponentially suppressed, ${\sl Im} \, \delta \sim
e^{-b^2/v\alpha'}$. This effect can be clearly seen in the SYM
truncation of the one-loop amplitude, where the norm of the outgoing
wavefunction is
\cite{Bachas,DKPS}
\begin{equation}
\vert\psi\vert^2=\tanh^8 \left( \frac{b^2}{4\alpha' v} \right)\,.
\end{equation}

Of course for string creation to be possible there must be enough
kinetic energy in the first place.  So we see that there are two
requirements for significant string creation to be possible,
\begin{equation}
\label{eq:CreationConditions}
b < 2 \sqrt{v \alpha'} \qquad \hbox{\rm and} \qquad
b < 2 \pi \alpha' {m_s \over 2 g_s} v^2\,.
\end{equation}
The second condition is the more stringent one when the relative
velocity is small.\footnote{These are semiclassical estimates.  The
small velocity regime, where the second condition dominates, really
calls for a fully quantum mechanical treatment of the D0 -- D0 system.
Such a treatment shouldn't change the qualitative behavior that string
creation vanishes as the relative velocity goes to zero.  We thank
C.~Bachas for raising this issue.}

The second mechanism for absorption we refer to as tachyon instability
\cite{BanksSusskind}.  While there is always a term $e^{-b^2s}$ in the
integrand for the phase shift, it could happen that for large $s$ the
function $f(s,v)$ behaves like $e^{+c^2s}$.  In eikonal scattering
this happens when the oscillator ground state energy of the stretched
string is negative.  Then for $b < c$ the proper time integral for the
phase shift diverges.  But by analytically continuing one sees that
what actually happens is the phase shift acquires an imaginary part.

Once a tachyon instability develops, the tachyon field will tend to
condense.  In a sense this condensation can be viewed as string
creation, since a coherent state of stretched strings is produced (the
strings just happen to have negative energy).  But this picture of
tachyons as stretched strings can be somewhat misleading in M(atrix)
theory.  In the context of SYM calculations the tachyon instability
arises when the (mass)$^2$ matrix for the off-diagonal elements has a
negative eigenvalue.  Of course the full potential ${\rm Tr}[{\bf
X}_i,{\bf X}_j]^2$ has a quartic piece that stabilizes the tachyon
field at some finite value.  When the tachyons condense, they lower
the energy of the original configuration.  They do this by making the
off-diagonal elements larger, which naively means that additional
strings are being added to the configuration.  But after the tachyons
condense, one can rediagonalize the matrices.  One finds that the
final configuration can be reinterpreted as having fewer stretched
strings present than the initial state.  Related phenomena have been
discussed in string theory \cite{Narain,Sen}.

In view of this ambiguity, we will use the term `string creation' only
in reference to the pair production of open strings with positive
energy arising from poles in the integrand.  A point which will be
important is that, even if no tachyon is present, string creation is
enhanced when $c^2$ is positive.  This is because the requirements for
string creation (\ref{eq:CreationConditions}) are relaxed to have
the form
\begin{equation}
\label{eq:CreationConditionsII}
b < \sqrt{4 \alpha' v + c^2} \qquad \hbox{\rm and} \qquad
b < 2 \pi \alpha' \left({m_s \over 2 g_s} v^2 + c\right)
\end{equation}
Thus string creation becomes possible for a wider range of impact
parameters when $c^2$ is positive.

\section{Horizons in gauge theory}

An essential feature of classical black holes is that they have an
event horizon.  That is, there is a region of spacetime from which one
cannot escape back to future infinity.  This means that classically
once an object enters the horizon it will be absorbed with certainty.

We want to understand how this happens in gauge theory.  In principle
given the wave function of a black hole state in the gauge theory we
could compute its absorption cross-section.  This absorption could
arise from one or both of the mechanisms discussed above.  We first
discuss Schwarzschild black holes, then briefly discuss the extremal
case.

\subsection{Schwarzschild black holes}

To mimic the black hole, we expect absorption to set in at a
relatively sharp radius, which should not depend on the nature of the
probe.  In particular the absorption cross section should be
approximately independent of the incoming probe momentum.  As we will
see, this is a non-trivial requirement.

We first consider string creation as a possible mechanism, and ask
whether string creation by gas of 0-branes (treated as distinguishable
particles) can be responsible for absorption by a Schwarzschild black
hole at the BFKS point.  The criterion is that if we send in a probe
0-brane with transverse momentum $p_\perp$ at an impact parameter
smaller than the Schwarzschild radius it should be
absorbed.\footnote{At the BFKS point a single 0-brane can be used to
probe a Schwarzschild black hole without much momentum transfer.}
This depends on the mean free path of a 0-brane in the gas of 0-branes
making up the black hole. The mean free path is given by
\begin{equation}
d =\frac{1}{n \sigma}
\end{equation}
where $n$ is the number density of the gas and $\sigma$ is the
absorption cross-section.  To estimate $\sigma$ we use the string
creation conditions (\ref{eq:CreationConditions}).  If the velocity is
large then the absorption radius $b \sim \sqrt{v}$ and hence $\sigma
\sim p_\perp^4$, while at small velocity $b \sim v^2$ so $\sigma \sim
p_\perp^{16}$.  The key point is that the probability of string
creation vanishes as the relative velocity goes to zero.
\footnote{These estimates are for eleven dimensional black holes.  In
D spacetime dimensions $\sigma$ behaves as $p_\perp^{(D-3)/2}$ and
$p_\perp^{2(D-3)}$, respectively.}

The condition for absorption is that the mean free path be smaller
than the Schwarzschild radius, $d < R_S$.  Using the BFKS density $n
\sim 1/l_p^9$ this translates into a lower bound on the transverse
momentum of the probe.  For large black holes it is the $\sigma \sim
p_\perp^{16}$ estimate which controls the bound: a probe must have
\begin{equation}
p_{\perp} > (R_S)^{-1/16}
\end{equation}
in Planck units to be absorbed.  This is rather unsatisfactory.  It
would indicate that a Schwarzschild black hole with radius $10^{38}
l_p \sim 1.6 {\rm km}$ can only absorb particles with momenta larger
than $4 \times 10^{-3} m_{p} \sim 10^{16} {\rm GeV}$.

This seems to rule out pure string creation as a mechanism for
absorption by the black hole.  But one can consider the following
hybrid mechanism.  Recall from (\ref{eq:CreationConditionsII}) that,
even if no tachyon develops, string creation is enhanced when the
oscillator ground state energy of a stretched string is negative.
Basically this makes the string lighter so it is easier to pair
produce them.  One could imagine that this enhances string creation to
the point where it is responsible for absorption by the black hole.

Such an effect is very plausibly present in non-extremal M(atrix)
black holes, as our examples in section 4 will show.  But given that
negative oscillator ground state energies are present and seem to play
a significant role, it is natural to imagine that a full-blown tachyon
instability might be present.  So let us look more closely at the
tachyon instability as an absorption mechanism.

Once a probe 0-brane enters the tachyon region, the tachyon mode will
start to condense and roll down its potential.  In the process it
acquires kinetic energy.\footnote{Quite unlike the string creation
scenario where much of the initially available energy is used up in
creating the string.}  But the tachyon field is coupled non-linearly
to the other degrees of freedom making up the black hole via the ${\rm
Tr} [{\bf X}_i,{\bf X}_j]^2$ interaction, so this energy is available
for distribution among all black hole degrees of freedom.  This is the
process of absorbing and thermalizing the new matter that fell into
the black hole.

One might worry that the probe 0-brane will leave the unstable region
before the tachyon condenses. The time scale for the tachyon to start
rolling down the potential is $t_0 \sim 1/ \sqrt{-m_{tachyon}^2}$.
Unless the probe just grazes the horizon, in order not to be captured
it must have a velocity of at least $v \sim R_{s}/t_0$.  At such large
velocities our quasistatic treatment of the background isn't reliable,
although we note that at very high velocities string creation could be
an important effect.  One also might worry that the energy which is
released by tachyon condensation could eject one of the other 0-branes
from the black hole.  But this is very unlikely at large $N$, when
there are many degrees of freedom present that can share the energy.

Of course 0-branes do escape from the black hole as Hawking particles
\cite{BFK}.  It would be interesting to understand how the tachyon
instability affects this process.  Suppose a particular 0-brane is
liberated, in that the strings connecting it to the rest of the black
hole happen to fluctuate to zero (either thermally or quantum
mechanically).  If this happens inside the tachyon region, then it is
still classically almost impossible for the 0-brane to escape the
black hole.  It is as if the 0-branes have to tunnel out of the
tachyon region in order to escape.

Note that the tachyon instability does not depend sensitively on the
relative velocity of the probe and target -- it is an effective
absorption mechanism even if the probe has zero velocity.  The tachyon
instability does depend crucially on the structure of the target,
however, and it is plausible that it could distinguish graviton states
(which do not have horizons) from Schwarzschild black holes (which
do), even though holography dictates that both gravitons and black
holes in a sense grow with $N$.

We feel that these properties make a tachyon instability an attractive
mechanism for absorption by a Schwarzschild black hole.  It seems
natural to associate the tachyon region with the size of the black
hole horizon.  To make this plausible, we must show that tachyon
instabilities can arise in macroscopically large regions in M(atrix)
theory.  We will do this in section 4 through consideration of some
explicit examples.

\subsection{Extremal black holes}

When a D-brane is used to probe an extremal black hole, absorption
should still set in at the horizon.  But the physical mechanism for
absorption must be different from the Schwarzschild case, since a
(supersymmetric) probe can't develop a tachyon instability.

An explicit example of such a system was studied in
ref.~\cite{DouglasPolchinskiStrominger}.  These authors used a
D1-brane to probe an extremal black hole with three charges, D1, D5,
and momentum.  One observation they made is that the horizon should be
identified with the origin of the Coulomb branch of the probe gauge
theory\footnote{This follows from the fact that in supergravity, in a
coordinate system with the horizon at $\rho=0$, they found that the
effective action for the probe has a term $f(\rho) \left(d\rho^2 +
\rho^2 d\Omega^2\right)$.  But a term of the same form arises in the
effective action on the Coulomb branch of the gauge theory, with
$\rho=0$ interpreted as the origin of the Coulomb branch.  Note the
contrast to the non-extremal case, where the horizon is located away
from the origin of moduli space \cite{MaldacenaProbe}.}.  They studied
geodesic motion on this moduli space, and argued that certain geodesics
which fall in towards $\rho=0$ are a signal of eventual absorption by
the black hole.

Unlike Schwarzschild black holes, the mechanism responsible for
absorption at the horizon of an extremal black hole cannot be a
tachyon instability.  Instead the mechanism is more plausibly one of
string pair creation.  Consider geodesic motion of a probe towards the
origin of moduli space.  The probe must have some non-zero velocity
$v$.  Then sufficiently close to the origin string creation will
become possible and the moduli space approximation will break
down\footnote{The one-loop estimate is that this occurs at $\rho =
\sqrt{v \alpha'}$.}.  String creation gives rise to an absorptive part
of the scattering amplitude, and can lead to capture of the probe by
the black hole (in gauge theory terms a transition from the Coulomb to
the Higgs branch).  As discussed above, string pair creation has a
slow rate of thermalization, since no energy is released in the
process.  But this is consistent with the black hole being extremal.

\section{Examples of tachyon regions}

In this section we calculate the tachyon instability region (TIR) in
some explicit M(atrix) configurations.  Ideally we would perform this
calculation for states corresponding to gravitons and Schwarzschild
black holes.  But our lack of precise knowledge of these wavefunctions
forces us to turn to some simpler examples, which we nonetheless feel
point out some general features of the TIR.  Our purpose is to make it
plausible that tachyons are present in M(atrix) theory, in macroscopic
regions that can be associated with Schwarzschild black holes.

The general calculational framework is as follows.  We choose an $N
\times N$ target configuration $B_i$, and place a 0-brane probe at a
position $b_i$.  This corresponds to a background in M(atrix) theory
\[
<{\bf X}_i> = \left[
\begin{array}{cc}
B_i & 0 \\
0 & b_i
\end{array}
\right] \,.
\]
The covariant gauge-fixed action of the M(atrix) quantum mechanics is
\cite{ClaudsonHalpern}
\begin{eqnarray*}
{\cal S} & =& \frac{1}{g_{YM}^{2}} \int dt \, {\rm Tr}
\left( D_t {\bf X}_i D_t {\bf X}_i +
\frac{1}{2}[{\bf X}_i,{\bf X}_j]^2
+ i \Psi_a D_t \Psi_a - \Psi_a \gamma_{ab}^{i}[{\bf X}_i,\Psi_b]\right) \\
& & \qquad \qquad
+ {\cal L}_{\hbox{\small gauge fixing}} + {\cal L}_{\hbox{\small ghost}}\,.
\end{eqnarray*}
Expanding the action around the background to quadratic order gives
the following (mass)$^2$ matrices for the off-diagonal degrees of
freedom connecting the probe to the target (see for example
\cite{KabatTaylor}).
\begin{eqnarray}
\label{eq:TheMasses}
M^2_{\rm YM} & = & \left[
\begin{array}{cc}
\sum_k \left(B_k - b_k\right)^2 & -2 \partial_t \left(B_j - b_j \right)\\
\noalign{\vskip 1mm}
2 \partial_t \left(B_i - b_i \right) & \hskip 1mm  \delta_{ij} \sum_k
\left(B_k - b_k\right)^2 + 2 [B_i,B_j]
\end{array}
\right] \\
\noalign{\vskip 0.2 cm}
M^2_{\rm fermi} & = & \sum_i (B_i-b_i)^2 \otimes {\rlap{1} \hskip 1.6pt \hbox{1}}_{16 \times 16}
+ i \partial_t \left(B_i - b_i\right) \otimes \gamma^i + {1 \over 2} [B_i,B_j]
\otimes \gamma^{ij}
\nonumber \\
\noalign{\vskip 0.2 cm}
M^2_{\rm ghost} & = & \sum_i (B_i-b_i)^2
\nonumber
\end{eqnarray}

We want to identify the probe positions which give rise to at least
one negative (mass)$^2$ eigenvalue.  Clearly $M^2_{\rm ghost}$ is
positive definite so we do not need to worry about the ghosts.  As
long as the background is static $M^2_{\rm fermi}$ is also the square
of a Hermitian matrix and hence is positive definite.  So tachyons do
not arise in the fermion sector and we can ignore them as
well.\footnote{In the context of string theory this is because the
Ramond sector always has zero oscillator ground state energy.}

This leaves the Yang-Mills degrees of freedom.  If the background is
time independent then $A_0$ does not mix with ${\bf X}_i$, and we only
need to consider the following $9N \times 9N$ (mass)$^2$ matrix for
the ${\bf X}_i$ degrees of freedom.
\begin{equation}
\label{eq:MassMatrix}
\left(M^2\right)_{ij} = \delta_{ij} \sum_k \left(B_k - b_k\right)^2
+ 2 [B_i,B_j]
\end{equation}
Even if the background does depend on time, dropping $A_0$ in this way
sets a lower bound on the size of the region with tachyons: given an
$n \times n$ Hermitian matrix with smallest eigenvalue $\lambda_{\rm
min}$, deleting one row and one column of the matrix produces a new
$(n-1) \times (n-1)$ matrix whose smallest eigenvalue is larger than
$\lambda_{\rm min}$ \cite{GR}. So for the rest of the paper we will
only analyze the mass matrix (\ref{eq:MassMatrix}).

More generally, in situations where the target must be treated quantum
mechanically, we can promote (\ref{eq:MassMatrix}) to an operator
equation.  That is, we can promote the classical background $B_i$ to a
$u(N)$-valued quantum operator ${\bf X}_i$, and write
\footnote{From now on ${\bf X}_i$ will denote the $N \times N$
operator corresponding to the target, not to be confused with the full
$(N+1)\times(N+1)$ M(atrix) field.}
\begin{equation}
\label{eq:QuantumMassMatrix}
\left(M^2\right)_{ij} = \delta_{ij} \sum_k \left({\bf X}_k - b_k\right)^2
+ 2 [{\bf X}_i,{\bf X}_j]
\end{equation}
where $[\cdot,\cdot]$ denotes the commutator in $u(N)$.  A tachyon
instability is present if the expectation value $<\psi \vert M^2 \vert
\psi>$ has a negative eigenvalue.  This can be regarded as a proposal
for defining the quantum horizon radius operator for a Schwarzschild
M(atrix) black hole.

\subsection{An $N = 2$ example}

We start by considering the case $N=2$.  This is mainly a warm-up to
illustrate some properties of the TIR.  An interesting feature which
will emerge is that the TIR does not have to be connected.

We consider backgrounds of the following form, involving two 0-branes
and some stretched strings.
\begin{eqnarray}
{\bf X}_1(t) & = & a_1(t) \sigma^{3} \\
{\bf X}_2(t) & = & a_2(t) \sigma^{1}
\label{bac1}
\end{eqnarray}
The $\sigma^i$ are Pauli matrices.  In general the operators $a_1(t)$,
$a_2(t)$ obey Heisenberg equations of motion, but for illustrative
purposes we will assume that there is some classical time-independent
background
\begin{eqnarray}
B_1 & = &  a_1 \sigma^{3} \\
B_2 & = &  a_2 \sigma^{1}
\end{eqnarray}
that approximates the properties of the state we are interested in.
The constants $a_1$, $a_2$ which appear in the background can be
thought of as suitable time averages of quantum expectation values.

The mass matrix for the bosons has the form
\[
M^2 =\left(
\begin{array}{cc}
C & 2D \\
-2D & C
\end{array}
\right)
\]
where $C$ and $D$ are $2 \times 2$ matrices.
\begin{eqnarray}
C & = &(a_1^2 +a_2^2 +b_{1}^{2} +b_{2}^{2}) {\rlap{1} \hskip 1.6pt \hbox{1}} +2a_1b_1 \sigma^3 +
2a_2b_2 \sigma^1 \\
D & = & 2ia_1 a_2\sigma^2
\end{eqnarray}
We want to find the region in $(b_1,b_2)$ space where the probe has a
tachyon instability, {\em i.e.} where $M^2$ has a negative eigenvalue.
The boundary of this region can be found by looking for zeroes of the
determinant.  Without loss of generality we assume $a_2^2>a_1^2$, and
find that the tachyon region is
\begin{eqnarray}
0\leq b_{1}^{2} \leq \sqrt{12a_1^2 a_2^2 +4(a_2^2-a_1^2)b_{2}^2}-a_2^2-
b^{2}_{2}+a_1^2 \\
{\rm max}\left(0,a_2^2-a_1^2 -\sqrt{12}a_1a_2\right) \leq b_{2}^2 \leq
a_2^2-a_1^2 +\sqrt{12}a_1a_2
\end{eqnarray}
The maximum of $b_{1}^{2}$ is
\begin{equation}
{\rm max}\left(\frac{3a_1^2 a_2^2}{a_2^2-a_1^2},
\sqrt{12}a_1a_2-a_2^2+a_1^2\right)
\end{equation}
If $a_1=a_2$ then there is a tachyonic instability in a disk of radius
$b^2=\sqrt{12} a_1^2$.  If $a_2^2-a_1^2-\sqrt{12}a_1a_2 > 0$ then
there are two distinct regions in which there is a tachyonic
instability.  If $a_2^2 \gg a_1^2$ then the TIR consists of two
regions, each roughly a circle of radius $\sim a_1$, centered at
$(0,a_2)$ and $(0,-a_2)$.

To look more precisely at the imaginary part, let us compute the phase
shift of a 0-brane scattered from this configuration.  To simplify
things we will take the impact parameter $b$ to be in the $x^3$
direction (and not as before in directions $x^1\,x^2$), and give the
probe 0-brane velocity $v$ in direction $x^4$. In this case there is
still string creation and a tachyonic instability so this simple
example serves to illustrate the general case.  Diagonalizing the
(mass)$^2$ matrices (\ref{eq:TheMasses}) leads to the one-loop phase
shift
\begin{eqnarray}
\label{pm}
\delta(b,v) & = & \int \frac{ds}{s} \, e^{-(b^2+a_{1}^{2}+a_{2}^{2})s}
\frac{1}{\sin sv} \, (4+2\cosh 4a_{1}a_{2}s
+2\cos 2sv \\
& & \qquad \qquad \qquad \qquad \qquad
-8\cos sv \cosh 2a_{1}a_{2}s)\nonumber
\end{eqnarray}
and there is a tachyonic instability for $b^2 < 4a_{1}a_{2}-a_{1}^{2}-a_{2}^{2}$.
Notice that there is no tachyon in the
fermionic sector (the last term in equation(\ref{pm})).  From
equation (\ref{pm}) the norm of the outgoing wave function of the
scattered 0-brane can be computed to give
\begin{equation}
|\psi_{out}|=\frac{(\cosh \frac{\pi r^2}{v}-\cosh \frac{\pi c}{v})^4}{8\cosh^{6}
\frac{\pi r^2}{2v}
(\cosh \frac{\pi r^2}{v}+\cosh \frac{2\pi c }{v})}
\label{no}
\end{equation}
where we have put $r^2=b^2+a_{1}^{2}+a_{2}^{2}$ and $c=2a_{1}a_{2}$.
Let us look at equation (\ref{no}). If $a_{2}=0$ then we are reduced
to scattering one 0-brane from two other 0-branes with the usual
answer of $\tanh^{8} \left(\pi b^2/v\right)$.  In the small $v$ limit
if $r^2<4a_1 a_2$
the norm of the wave function is $\sim 0$.
Furthermore, even for small $v$ and $r^2$ outside
tachyonic region, if $r^2-4a_{1}a_{2} \sim v$ then the norm of the
wave function is $\sim 1/4$ signaling the enhancement of
string creation close to (but outside) a TIR.

\subsection{Spherical membranes}

The next set of examples we consider are spherical membranes
\cite{GoldstoneHoppe,dhn,KabatTaylor,Rey}.  A round spherical
membrane of radius $r$ can be described in M(atrix) theory by setting
\begin{equation}
B_i = \left\lbrace
\begin{array}{ll}
{2 \over N} r J_i & i=1,2,3 \\
0 & {\rm otherwise}
\end{array}
\right.
\label{eq:SphericalMembrane}
\end{equation}
The sphere is centered at the origin and extends in the directions
$x^1\,x^2\,x^3$.  The matrices $J_i$ are generators of $SU(2)$ in the
$N$-dimensional representation, normalized to satisfy
\[
[J_i,J_j] = i \epsilon_{ijk} J_k \qquad
\sum_i J_i^2 = {N^2 - 1 \over 4} \, {\rlap{1} \hskip 1.6pt \hbox{1}}\,.
\]
We take the radius of the membrane to be much larger than the Planck
length, so that this background can be treated semiclassically.  The
M(atrix) equations of motion imply that the membrane starts to
collapse.  Eventually it will fall through its Schwarzschild radius
and form a black hole.  But black hole formation seems out of reach of
the semiclassical approximation, so we will study the membrane only
when it is at its initial (maximal) radius, with ${dr \over dt} = 0$.
This is feasible at large $N$ because the time to collapse increases
linearly with $N$ (the formula is given in \cite{KabatTaylor}).

The M(atrix) background (\ref{eq:SphericalMembrane}) is a good
approximation to a well-behaved state which is present in the full
M-theory.  It corresponds to a fundamental membrane, which has a
degenerate horizon.  In accord with this, we will verify that the
region with tachyons for these matrices vanishes in the large $N$
limit.  This does provide evidence for the hypothesis that the TIR
should be associated with the size of the horizon.

We place a probe at a position $b_i$, which we take for simplicity to
be non-zero only in the first three coordinates.  Inserting the
membrane background (\ref{eq:SphericalMembrane}) into the (mass)$^2$
matrix (\ref{eq:MassMatrix}), one finds that the non-trivial
eigenvalues come from the $3N \times 3N$ block
\[
\left(M^2\right)_{ij} = \left(r^2\left(1-1/N^2\right)
+ \vert b \vert^2\right) \delta_{ij} {\rlap{1} \hskip 1.6pt \hbox{1}}_{N \times N}
- {4 \over N} r b \cdot J \delta_{ij}
+ i {8 r^2 \over N^2} \epsilon_{ijk} J_k
\]
where the indices $i,j,k = 1,2,3$.

Finding the exact eigenvalues of this matrix is a difficult problem.
But, at leading order in $1/N$, one can proceed as if the different
SU(2) generators commute.  Treating the $J_i$'s as if they were
numbers, and diagonalizing, one finds that the lowest eigenvalue comes
from an $N \times N$ block given by
\[
-{4 \over N} r b \cdot J - {8 r^2 \over N^2} \sqrt{J_1^2 + J_2^2 + J_3^2}\,.
\]
In turn diagonalizing this block, one finds that the smallest eigenvalue
of $M^2$ is
\[
\lambda_{\rm min} = \left(\vert b \vert - r (1-1/N)\right)^2 - 2 r^2 / N^2
\]
where we dropped terms of order $1/N^3$.  So the smallest
eigenvalue is negative if the probe is located in the region
\[
r\left(1-1/N\right) - \sqrt{2} r / N \, < \, \vert b \vert \, < \,
r\left(1-1/N\right) + \sqrt{2} r / N\,.
\]
That is, tachyons are present in a region which is centered at
roughly the radius of the sphere, $\vert b \vert \approx r$, and
extends in either direction to form a shell of thickness $\sim r/N$.
In the large $N$ limit the region with tachyons disappears.  This is
in accord with our expectations, since the fundamental membrane of
M-theory has a degenerate horizon.

The closely related example of a 0-brane probing a toroidal membrane
was studied in \cite{AharonyBerkooz,LifschytzMathur}.

\subsection{Gaussian Random Matrices}

To motivate this final example, we observe that a precise understanding of
the relationship between M(atrix) theory tachyons and Schwarzschild
black hole horizons would require finding the black hole wavefunction
$\psi_{\rm hole}({\bf X}_1,\ldots,{\bf X}_9)$.  Then we could compute the
expectation value of the (mass)$^2$ matrix
\[
<M^2> = \int d^{\,9}{\bf X} \, \psi_{\rm hole}^*({\bf X}) M^2
\psi_{\rm hole}({\bf X})
\]
and find its lowest eigenvalue as a function of the position of the
probe.  If our proposed identification is correct, the lowest
eigenvalue should become negative when the probe is exactly at the
Schwarzschild radius.

In attempting this, we are hampered by our poor understanding of the
black hole wavefunction.  Although many of its properties have been
discussed in the literature
\cite{BFKS,KlebanovSusskind,Halyo,HorowitzMartinec,Li,DMRR,BFKS2,BFK,OhtaZhou,LiMartinec},
it is not understood precisely enough to make a calculation of $<M^2>$
possible.  Nonetheless, several general properties which the
wavefunction of a Schwarzschild black hole should satisfy are clear.
\begin{enumerate}
\item
At the BFKS point the wavefunction should have support on matrices
${\bf X}_i$ whose eigenvalues fall within a finite range.  The range of the
eigenvalues is presumably of order the Schwarzschild radius.
\item
A Schwarzschild black hole is spherically symmetric, so the wavefunction should
be invariant under $SO(9)$ rotations ${\bf X}_i \rightarrow R_{ij} {\bf X}_j$.
\item
The gauge symmetry of M(atrix) theory requires that the wavefunction be
invariant under unitary transformations ${\bf X}_i \rightarrow U^\dagger
{\bf X}_i U$.
\end{enumerate}

Our strategy is to compute the distribution of eigenvalues of
$M^2$, not with respect to the true probability distribution
given by solving M(atrix) theory
\[
P({\bf X}_1,\ldots,{\bf X}_9) = \psi^*_{\rm hole}({\bf X})
\psi_{\rm hole}({\bf X}),
\]
but rather with respect to the Gaussian probability distribution
\[
P({\bf X}_1,\ldots,{\bf X}_9) = {\rm const.} \,\,\, {\rm exp}
\left(-{1 \over 2 \sigma^2} {\rm Tr} \sum_i {\bf X}_i^2\right)\,.
\]
We regard the width of the Gaussian $\sigma$ as a freely adjustable
parameter.

The Gaussian ensemble in fact satisfies the general properties
expected of a black hole listed above.  The fact that the ensemble
is $SO(9) \times U(N)$ invariant is obvious.  Also, for large $N$ the
distribution of eigenvalues of any one of the matrices ${\bf X}_i$ is
given by a Wigner semicircle
\begin{equation}
\rho(\lambda) = {1 \over 2 \pi N \sigma^2} \sqrt{4 N \sigma^2 - \lambda^2}\,.
\label{eq:Wigner}
\end{equation}
The large-$N$ limit is taken with the 't Hooft coupling $\sigma^2_{\rm eff}
\equiv N \sigma^2$ held fixed, so that the eigenvalues of the matrices
${\bf X}_i$ all lie within the finite interval
\begin{equation}
\label{eq:WignerRange}
-2 \sigma_{\rm eff} \le \lambda \le 2 \sigma_{\rm eff} \,.
\end{equation}

Since the Gaussian ensemble has some key features of a
Schwarzschild black hole, we expect that studying the tachyon region
in the Gaussian ensemble will point out some of the qualitative
effects which would be present in a more realistic M(atrix) theory
calculation.  Indeed, an optimist could even hope to use the Gaussian
ensemble as a reasonable variational approximation to the true black
hole wavefunction at the BFKS point \cite{KabatLifschytz}.

The practical advantage of Gaussian ensembles is that they are
relatively easy to work with.  Although we have not managed to find
the exact region with tachyons in the Gaussian ensemble, we are able
to put strict bounds on it as follows.  Write the (mass)$^2$ matrix as
a sum of two pieces.
\begin{eqnarray*}
M^2 & = & A + B \\
A_{ij} & \equiv & \delta_{ij} \sum_k {\bf X}_k^2 + 2 [ {\bf X}_i, {\bf X}_j] \\
B_{ij} & \equiv & \delta_{ij} \left(\vert b \vert^2 - 2 \sum_k b_k {\bf X}_k\right)
\end{eqnarray*}

First we study the eigenvalue distribution of the matrix $A$, which corresponds to placing
the probe at the origin (setting $b=0$).  It is convenient to work with
dimensionless eigenvalues ${\tilde{\lambda}}$ defined by ${\tilde{\lambda}} = \lambda/\sigma^2_{\rm eff}$.
We introduce the resolvent
\[
{\cal R}_A({\tilde{\lambda}}) = {\sigma^2_{\rm eff} \over 9 N} \, {\rm Tr} \langle {1 \over \sigma^2_{\rm eff} {\tilde{\lambda}} - A} \rangle\,.
\]
The normalized distribution of eigenvalues $\rho_A({\tilde{\lambda}})$ can be obtained
from the resolvent via
\[
\rho_A({\tilde{\lambda}}) = - {1 \over \pi} {\rm Im} \, {\cal R}_A({\tilde{\lambda}} + i \epsilon)
\]
as a consequence of the identity ${1 \over x + i \epsilon} = {\rm P.V.}
{1 \over x} - i \pi \delta(x)$.
In the appendix we show that the resolvent, computed at leading order in $1/N$,
satisfies the following cubic equation.
\begin{equation}
73 {\tilde{\lambda}} {\cal R}_A^3 + 584 {\cal R}_A^2 + 9 (9-{\tilde{\lambda}}){\cal R}_A + 9 = 0
\label{eq:cubic}
\end{equation}
Of the three solutions to this equation, only one has a negative
imaginary part.  Solving for ${\cal R}_A$ and extracting the imaginary part
gives the eigenvalue distribution shown in Fig.~1.  As can be seen
from the graph, the lowest eigenvalue of $A$ is
\begin{equation}
\label{eq:Amin}
\lambda_A^{\rm min} \approx -8.0 \sigma^2_{\rm eff} \,.
\end{equation}
The key fact is that the lowest eigenvalue is {\em negative}.

\begin{figure}
\epsfig{file=tachyon_fig.ps}
\caption{The eigenvalue distribution $\rho_A({\tilde{\lambda}})$.  Equivalently, the
density of stretched string states vs.~(mass)$^2$ for a probe at the center
of a Gaussian ensemble.}
\end{figure}

The distribution of eigenvalues of the matrix $B$ can be obtained starting from the Wigner semicircle
(\ref{eq:Wigner}).  It is given by
\[
\rho_B({\tilde{\lambda}}) = {1 \over 8 \pi {\tilde{b}}^2} \sqrt{16 {\tilde{b}}^2 - \left({\tilde{\lambda}} - {\tilde{b}}^2
\right)^2}
\]
where the dimensionless probe position ${\tilde{b}}$ is defined
by ${\tilde{b}} = \vert b \vert/\sigma_{\rm eff}$.  Note that the eigenvalues
of $B$ lie in the interval
\begin{equation}
\label{eq:Brange}
{\tilde{b}}^2 - 4 {\tilde{b}} \, \leq \, {\tilde{\lambda}}_B \, \leq \, {\tilde{b}}^2 + 4 {\tilde{b}} \,.
\end{equation}

Having found the spectra of $A$ and $B$ separately, the lowest eigenvalue of
$M^2 = A + B$ can be bounded by
\begin{equation}
\lambda_A^{\rm min} + \lambda_B^{\rm min} \,\leq\, \lambda_{M^2}^{\rm min}
\,\leq\, \lambda_A^{\rm min} + \lambda_B^{\rm max}\,.
\label{eq:MinEigen}
\end{equation}
If $b=0$, so the probe is located at the origin,
then the matrix $B$ vanishes, and the eigenvalue distribution of $M^2$ is given in Fig.~1: a probe
0-brane placed at the center of a Gaussian ensemble has many tachyonic modes.  As $\vert b
\vert$ increases the eigenvalues of $M^2$ tend to increase, and
eventually a critical radius is reached at which there are no more
tachyons.  Applying the inequality (\ref{eq:MinEigen}) to the results
(\ref{eq:Amin}), (\ref{eq:Brange}) we can say that the smallest
eigenvalue of $M^2$ lies in the range
\begin{equation}
{\tilde{b}}^2 - 4 {\tilde{b}} - 8.0 \,\leq\, {\tilde{\lambda}}_{M^2}^{\rm min} \,\leq\,
{\tilde{b}}^2 + 4 {\tilde{b}} - 8.0\,.
\label{eq:Mmin}
\end{equation}
It then follows that the critical
tachyon radius, at which the smallest eigenvalue of $M^2$ vanishes,
lies somewhere in the interval $1.47 < {\tilde{b}}_{\rm crit} < 5.47$.  Restoring units,
this reads
\[
1.47 \sigma_{\rm eff} < \vert b \vert_{\rm crit} < 5.47 \sigma_{\rm eff} \,.
\]

Recall from (\ref{eq:WignerRange}) that the largest
eigenvalue of the matrices ${\bf X}_i$ is $2 \sigma_{\rm eff}$.  So we
see that the tachyon instability sets in at roughly the same radius as
the size of the object defined by its range of eigenvalues.

\section{Conclusions}

We have argued that the horizon of a Schwarzschild black hole (or more
precisely, a trapped surface) is seen by a 0-brane probe in M(atrix)
theory as a critical radius at which a tachyon develops.  This gives
an interesting picture of the process by which such a black hole is
formed.  One starts with a collection of 0-branes located far from
each other.  With the right initial momenta they will approach each
other and some string creation will take place.  If enough strings are
created then a tachyon region will form. If the size of the tachyon
region is $\gg l_{p}$ then a macroscopic black hole has been created.
If another 0-brane approaches the black hole, it will be absorbed when
it enters the tachyon region.  In the absorption process the tachyon
rolls down its potential and, via its couplings to the other 0-branes
making up the black hole, thermalizes the infalling matter.

Since we do not have good control over the wavefunction of a
Schwarzschild black hole, we cannot conclusively show that it has a
tachyon region.  But by analyzing some examples where a tachyon
instability arises in M(atrix) theory, we showed that the TIR has
reasonable properties to be an indicator for a Schwarzschild horizon.
We gave examples which have macroscopic tachyon regions, even in the
large $N$ limit.  We also studied membrane states, where the TIR
vanishes at large $N$.

The most interesting example we analyzed was the tachyon instability
for Gaussian random matrices.  In this large-$N$ calculation we showed
that the size of the tachyon region is roughly the same as the spread
of 0-brane positions.  It is conceivable that the Gaussian ensemble is
a good variational approximation to the true wavefunction of a
Schwarzschild black hole at the BFKS point.  At least in the
non-supersymmetric case, Gaussians have been shown to give a fairly
good approximation for large-$N$ Yang-Mills quantum mechanics
\cite{EngelhardtLevit}.  The crucial test of this idea is to include
the fermions and compute the mass of a typical state in the Gaussian
ensemble \cite{KabatLifschytz}.

We expect that much of our discussion of tachyon instabilities can be
carried over to other non-extremal black holes built out of D-branes.
And given the conjectured relation between finite temperature SYM and
black holes in AdS space \cite{Maldacena}, our proposal suggests that
the phenomenon of tachyon instability can also be used as a gauge
theory indicator for the horizon of a non-extremal AdS black hole.

\vskip 1.0 cm
\centerline{\bf Acknowledgements}
We are grateful to Constantin Bachas, Misha Fogler, Anton Kapustin,
Igor Klebanov, Samir Mathur, Steve Shenker, and Lenny Susskind for
valuable discussions.  The work of DK is supported in part by the
Department of Energy under contract DE-FG02-90ER40542 and by a
Hansmann Fellowship. The work of GL is supported by the NSF under
grant PHY-91-57482.

redpajama_set_name: RedPajamaArXiv


text:
November 2019 (Regular Meeting)
PROCEEDINGS OF THE MEETING OF THE MAYOR AND BOARD OF ALDERMEN OF THE CITY OF BREAUX BRIDGE HELD AT THE CITY HALL, 101 BERARD STREET, AT 6:00 P.M. ON TUESDAY, NOVEMBER 12, 2019.
Present: Ryan Breaux, Scotty Borel, Ernest "E.J." Ledet, Neil Melancon and Eddy LeBlanc
Absent: None
Monthly budget-to-actual comparisons on the General Fund, Sales Tax Funds, Park and Recreation Fund, and Utility Funds were distributed to the Councilmen and Mayor.
Upon motion of Ernest Ledet duly seconded by Neil Melancon and unanimously carried, the minutes of the October 8, 2019 regular City Council meeting were approved.
Upon motion of Neil Melancon, duly seconded by Ryan Breaux and unanimously carried, the Board of Aldermen opened the public hearing on Ordinance #2255 (an Ordinance to amend Chapter 23 of the Code of Ordinances by the repeal, amendment, revision, enactment and/or re-enactment of Sections 23-5.19 through 23-5.19.16, and 23-7.8.15 regarding zoning regulations).
Planning and Zoning Director, Amanda LeBlanc gave a brief explanation of the changes in this Ordinance. The changes will affect Rees Street from Latiolais Street to Refinery Street on both sides, new subdivisions and any new buildings. We will have street lighting, plants, trees, etc. This pertains to new construction, any new retrogrades for development whether subdivisions and or commercial.
Mayor Ricky Calais stated that this is from the study that was done on the Rees Street Corridor. This is a document that we would adopt making official some of the changes and improvements we might want to pursue over the course of the next several years. Rees Street is the front door to our community and we want to make it as inviting and successful as possible.
Mike Hollier explained the process of the Rees Street study and its changes.
Upon motion of Ernest Ledet, duly seconded by Ryan Breaux and unanimously carried, the Board of Aldermen closed the public hearing on Ordinance #2255.
Upon motion of Eddy LeBlanc, duly seconded by Ryan Breaux and unanimously carried, the Board of Aldermen adopted Ordinance #2255.
ORDINANCE NUMBER 2255
An ordinance to amend Chapter 23 of the Code of Ordinances by the repeal, amendment, revision, enactment, and/or re-enactment of Sections 23-5.19 through 23-5.19.16 and Section 23-7.8.15 regarding zoning regulations.
BE IT ORDAINED by the Mayor and Board of Alderman for the City of Breaux Bridge, Louisiana duly convened in regular session on the 12th day of November 2019, that:
The Code of Ordinances for the City of Breaux Bridge, Louisiana be amended by the repeal, amendment, revision, enactment, and/or re-enactment of Sections 23-5.19 through 23-5.19.16 Section 23-7.8.15 as follows:
Sec. 23-5.19. – C-6, Rees Street Enhanced Arterial Commercial District.
The Comprehensive Plan identifies La. Hwy. 328/Rees Street as a Major Roadway in the community. A corridor design plan including underground utilities, street cross-sections, land use, access, drainage, signage, lighting, and buildings are critical considerations for long term development. Interstate Highway 10, Grand Point Highway, Main Street, and Rees Street are entirely different and uniquely configured roadways with land use improvements and needs very different in scope, character and regulation. The Comprehensive Plan notes the commercial area of Breaux Bridge now and into the future is focused on Rees Street. Design aesthetics, both public and private, should be and are recommended for special attention and consideration
Sec. 23-5.19.1. – Purpose.
The Comprehensive Plan emphasizes and reiterates importance and need for community character in future development. As a primary commercial roadway in the City of Breaux Bridge the Rees Street Enhanced Arterial Commercial Zoning District is established to address the physical development needs of this Major Roadway over the long term. The evolution of Rees Street over time is accomplished through the stated actions of the Comprehensive Plan. Protection and enhancement of property value investment through land use, multi-modal transportation infrastructure, and community aesthetics are fundamental to meet desired Plan goals and objectives. The responsibilities of both public and private interests are centered on an Advanced Arterial Design for Rees Street defined and adopted by the Planning Commission and approved with support and implementation by the Board of Aldermen.
Sec. 23-5.19.2. – Definitions.
(a) Full Cut-off Lighting Fixture means a lighting fixture from which no light output is emitted at or above a horizontal plane drawn through the bottom of the lighting fixture.
(b) Banquette is a pedestrian way, path or sidewalk constructed parallel with a public street.
(c) Enhanced Street Front Public Servitude is a public servitude provided by the property owner fronting the public street for purpose of installation and maintenance of underground utilities, street trees, banquette, and commercial signage outside of the public street right-of-way.
(d) Sports Bar is characterized by a minimum number of twenty (20) direct on-line visual TV screens providing live action sporting events and food service with alcohol.
(e) High Density Residential is defined in this zoning district as a minimum of ten (10) residential units per acre placed on second floor or above in a single building.
(f) Street Tree will be recommended by Mayor or appointed committee.
(g) Joint Access Servitude is the legal agreement document between two adjacent property owners allowing joint public access from a public street for buildable lots of record.
(h) Monument Signs are permanent free-standing ground signs of monolithic construction.
Sec. 23-5.19.3. – Permitted Uses.
The Rees Street Enhanced Arterial Commercial Zoning District allows for a mix of commercial land uses including medical service, business office, general retail, restaurants, entertainment and athletic centers, equipment sales, fueling stations, food centers, department stores, business services, parking garages, vehicle repair shops, sports bars, plant nursery sales, convenience stores, overnight camping/recreational vehicle parks, personal services, movie theaters, hotels, and motels. The zoning district allows for a select mix of high density residential provided above first floor ground commercial uses. Single family residential is allowable, but not encouraged.
Sec. 23-5.19.4. – Prohibited Uses.
The Rees Street Enhanced Arterial Commercial Zoning District prohibits light or heavy manufacturing, schools, public works, government services or facilities (except public parks and gateways), storage facilities, distribution centers, light or heavy industrial facilities or services, agriculture, bars/lounges (unless a minor service of a restaurant or "sports bar" as defined for the district), waste transfer facility, shipping container sales, animal kennels, environmental clean-up facilities, re-cycling centers, religious houses of worship, cemeteries, mobile homes, funeral homes, and nursing homes.
Sec. 23-5.19.5. – Requirements.
Rees Street (La. Hwy. 328) public and private infrastructure design and implementation is divided into three area levels of responsibility: (a) Louisiana Department of Transportation and Development (DOTD) for state highway right-of-way infrastructure – roadway, signal lights, roundabouts, curbing, drainage, medians, cross walks, bikeways, pavement, pavement markings, signage and turning lanes; (b) City of Breaux Bridge for street tree landscape, banquette, pedestrian lighting, transit stops, and transportation gateways; and (c) property owner, business owner, or developer for buildings, parking, joint access agreements, community icon, private landscaping, drainage retention, commercial signage, street address display and public servitudes.
1. The Rees Street Enhanced Arterial Commercial Zoning District applies to property adjacent to the roadway right-of-way for a maximum depth of eight hundred (800) feet or as noted on the official zoning map for the district.
2. Minimum Lot Area: None
3. Enhanced Street Front Public Servitude: Twenty (20) feet lot depth (from the roadway right-of-way into buildable lot of record) extending width of lot.
4. Side Yard Requirements: Seven (7) feet minimum which may be landscaped or hard surfaced.
5. Rear Yard Requirements: Seven (7) feet minimum including a vegetative buffer of five (5) feet planted with Hedge Bamboo, Bambusa Multiplex (a non-invasive variety with thick foliage), spacing five (5) feet on center.
6. City Infrastructure: When new development is approved for a buildable lot in the Rees Street Enhanced Arterial Commercial Zoning District, the City will plan to execute provision for installation of, pedestrian lights, banquettes (multipurpose path), and street trees located in the Enhanced Street Front Public Servitude of the buildable lot. The installation of these improvements shall be in accordance with the Rees Street Advanced Arterial Design Plan adopted cross section.
Sec. 23-5.19.6. – Major Roadway Network.
Rees Street is a designated State Highway Route – La. Hwy. 328 and is the responsibility of the Louisiana Department of Transportation and Development (DOTD). All infrastructure improvements within this state right-of-way are subject to DOTD review, approval and permitting. Rees Street/La. Hwy. 328 is identified as a Major Roadway on the Acadiana Metropolitan Planning Organization (MPO) Major Roadway Network (MRN). And, Rees Street is a major street corridor on the Transportation Element of the City of Breaux Bridge Comprehensive Plan. The three public entities have coordinated to develop and adopt the "Advanced Arterial Design" cross section plan for this important transportation link and commercial corridor within the City of Breaux Bridge. Prior to the issuance of any permit in the Rees Street Enhanced Arterial Commercial Zoning District for installation or construction, the final adopted "Advanced Arterial Design" (AAD) and its component parts must be considered and applied.
Sec. 23-5.19.7. – Landscaping.
Landscaping requirements for new development on a buildable lot in the zoning district is divided into two parts: (a) Public Street Trees placed by the City of Breaux Bridge in the Enhanced Street Public Servitude; and (b) Land owner landscaping, including buffer strip requirements comprising a total minimum of ten percent (10%) of the buildable lot.
Sec. 23-5.19.8. – Signage.
Signage in the Rees Street Enhanced Arterial Commercial Zoning District shall follow the general requirements established in Section 23-7.8 for signs in this ordinance with one fundamental exception: Free standing commercial signs are restricted to Monument Signs with a forty percent (40%) limitation of the sign face to Changeable Messaging.
Conformity Term Period: Free standing signs existing in the Rees Street Enhanced Arterial Commercial Zoning District are required to be in conformity with this Section of the zoning regulations not later than January 1, 2034.
Sec. 23-5.19.9. – Street Lighting.
The City of Breaux Bridge is responsible for lighting subject to permit review and approval by the Louisiana Department of Transportation and Development (DOTD).
Sec. 23-5.19.10. – Off-street Parking.
There are no "Off-Street" parking spaces required in the Rees Street Enhanced Arterial Commercial Zoning District. Should a property owner, business owner, developer, or resident request to include parking spaces on the approved buildable lot of record those parking spaces shall be identified and placed in the rear of the primary lot building and adjacent to and accessible by side lots of record. Side yard lot parking is allowable but may not constitute more than twenty percent (20%) of the total parking provided.
Sec. 23-5.19.11. – Building Exterior Materials.
The exterior (excluding roofs) of new buildings within the Rees Street Enhanced Arterial Commercial Zoning District shall consist of one or any combination of the following materials: brick, wood, glass, stucco, stone, or a specific durable material subject to approval by the Planning Commission.
Sec. 23-5.19.12. – Community Icon.
The Breaux Bridge community icon is the "Crawfish". New development within the Rees Street Enhanced Arterial Commercial Zoning District is encouraged to include this community icon visibly from the public street. There is no material, size or design standard for the required displayed icon other than it shall be recognizable and not abstracted. Developers shall submit details of the icon as part of development review and/or permitting. Property owners, business owners and developers are encouraged to utilize creative local artists whenever practical in meeting this requirement.
Sec. 23-5.19.13. – Banquette.
A seven (7) foot wide banquette/sidewalk/multipurpose path is planned within the Enhance Street Front Public Servitude to be constructed by the City of Breaux Bridge. Banquettes are required along all other streets within the Rees Street Enhanced Arterial Commercial Zoning District and built to general standards approved by the City of Breaux Bridge and provided by the property owner, business owner or developer where applicable.
Sec. 23-5.19.14. – Joint Access.
Joint access between and among adjacent property owners fronting on Rees Street is required. A legal joint access agreement template shall be provided to affected property owners based on submitted development plans which shall be made a part of approval and permitting. Joint access shall apply to Rees Street frontage access and rear/backage access.
The purpose of the Front Joint Access Agreement is to reduce curb cuts on the Major Roadway and improve capacity. The purpose of the Rear Joint Access Agreement is to provide for interconnectivity between approved buildable lots to accommodate traffic and development safety. The rear joint access servitude shall extend the width of the lot. Extenuating site circumstances may make joint access impractical and the planning commission may review and grant an exception to the joint access requirement when deemed appropriate.
Sec. 23-5.19.15. – Reserved.
Sec. 23-7.8.15. – Appeals.
Appeals to the Board of Adjustment may be taken by any party whose application for a permit has been denied under Sections 23-7.8. Such appeal shall be taken in accordance with Section 23-11.2, as may be amended, from time to time.
Requests for Variances or Adjustments to these regulations may be submitted to the Board of Adjustment through the appropriate application process which requires the applicant to identify the specific variance or adjustment to be addressed. The applicant must appear in person, not by proxy, before the Board of Adjustment for consideration of a variance or adjustment to these zoning regulations. Failure to so appear will render variance or adjustment consideration null and void. When a variance or adjustment is approved by the Board, that variance or adjustment shall be site specific, and shall not be a waiver of any aspects of this ordinance for other sites within the City of Breaux Bridge. Appeal of decisions of the Board of Adjustment (Board of Aldermen) may be filed with the District Court.
BE IT FURTHER ORDAINED by the Board of Aldermen for the City of Breaux Bridge, Louisiana, that all other ordinances and provisions of the Code of Ordinances for the City of Breaux Bridge, Louisiana, that are in conflict with the provisions hereof are hereby declared to be repealed to the extent any such conflict exists.
BE IT FURTHER ORDAINED by the Board of Aldermen for the City of Breaux Bridge, Louisiana, duly convened in regular session on the 12th day of November, 2019, that the provisions of this ordinance are hereby declared to be severable, and if any provision, word, phrase, or clause of this ordinance or the application thereof to any person or circumstance is held invalid, such invalidity shall not affect the validity of the remaining portions thereof.
UPON MOTION of Eddy LeBlanc, seconded by Ryan Breaux, and upon verification and assurance that the foregoing ordinance was:
Introduced on October 8, 2019, at the regular meeting of the Mayor and Board of Alderman for the City of Breaux Bridge, Louisiana;
Disseminated to the Mayor and all Aldermen;
Published, by title, in the official journal of the City of Breaux Bridge, Louisiana, together with the notice of the time and place of its consideration for formal adoption; and
Presented at a public hearing held on the 12th day of November, 2019,
The Board of Aldermen, on the 12th day of November, 2019, adopted Ordinance Number 2255 by virtue of the following votes:
YEAS: Ryan Breaux, Scotty Borel, Ernest "E.J." Ledet, Neil Melancon, Eddy LeBlanc
NAYS: None
ABSENTIONS: None
ATTEST: APPROVED:
______________________ ________________________
KRISTI LEBLANC, RICKY CALAIS,
Upon motion of Ernest Ledet, duly seconded by Ryan Breaux and unanimously carried, the Board of Aldermen opened the public hearing on Ordinance #2256 (An Ordinance to amend Chapter 23 of the code of Ordinances for the city of Breaux Bridge, Louisiana, by the repeal, amendment, revision, enactment, and/or reclassification of 23-5.16 through 23-5.16.9 adopted per Ordinance 2247 to Sections 23-5.17 through 23-5.17.9, regarding zoning regulations.)
City Attorney, Bart Hebert stated that this is not a new law. It is two ordinances that were passed with zoning regulations already but one overlapped the other in the numbering so basically we are moving the numbering to represent them accurately.
Upon motion of Neil Melancon, duly seconded by Ryan Breaux and unanimously carried, the Board of Aldermen closed the public hearing on Ordinance #2256.
Upon motion of Ernest Ledet, duly seconded by Neil Melancon and unanimously carried, the Board of Aldermen adopted Ordinance #2256.
An ordinance to amend Chapter 23 of the Code of Ordinances for the City of Breaux Bridge, Louisiana, by the repeal, amendment, revision, enactment, and/or reclassification of Sections 23-5.16 through 23-5.16.9 adopted per Ordinance 2247 to Sections 23-5.17 through 23-5.17.9, regarding zoning regulations.
BE IT KNOWN that Ordinance 2235 affecting various sections of the City's zoning regulations including, but not limited to, Sections 23-5.16 through 23-5.16.8, was adopted by the Board of Aldermen on December 12, 2017 and approved by the Mayor on December 12, 2017.
BE IT KNOWN that Ordinance 2247 affecting various sections of the City's zoning regulations including, but not limited to, Sections 23-5.16 through 23-5.16.9, was adopted by the Board of Aldermen on October 9, 2018 and approved by the Mayor on October 9, 2018.
BE IT KNOWN that through clerical error and inadvertence Ordinance 2247 incorrectly identified some new sections of the City's zoning regulations as Sections 23-5.16 through 23-5.16.9, when such sections should have been identified as Sections 23-5.17 through 23-5.17.9, and it is now necessary to correct this clerical error and reclassify those Sections as 23-5.17 through 23-5.17.9.
BE IT ORDAINED by the Board of Alderman for the City of Breaux Bridge, Louisiana duly convened in regular session on the 12th day of November, 2019, that:
Chapter 23 of the Code of Ordinances for the City of Breaux Bridge, Louisiana, adopted as Sections 23-5.16 through 23-5.16.9 as per Ordinance 2247 be reclassified as Sections 23-5.17 through 23-5.17.9, as follows:
Sec. 23-5.17. – Traditional Neighborhood Development District.
The purpose and guiding principles of the Traditional Neighborhood Development (TND) is create a range of housing opportunities and choices, create walkable neighborhoods, encourage distinctive, attractive design with a strong sense of place, include public and private sustainable infrastructure wherever possible, provide a variety of transportation options and preserve natural beauty and critical environmental areas. These desirable objectives are reiterated in the Breaux Bridge Comprehensive Plan and should accomplish cost effectiveness in both short term and long term physical and fiscal urban growth and development in the City.
A Traditional Neighborhood Development District is established for one of two purposes: Development of new neighborhoods, structured on a network of interconnecting pedestrian oriented streets and other public spaces. The TND provides a balanced mix of activities and has a recognizable center and clearly defined edges. The TND may also be used to redesign, redevelop (reinvigorate) and infill older existing urban neighborhoods.
(a) Binding Conditions: Property owners and/or developers submitting "Concept Review Plans" within the Zoning District may be approved subject to specific conditions binding on the property owner and/or developer for final plan approval and the issuance of any construction permits.
(b) Concept Review Plans: Land development proposals submitted to the Planning Commission for preliminary review and consideration prior to final review and approval.
(c) Lighting: All outdoor lighting fixtures, including without limitation, ground pole, and building mounted fixtures and canopy lighting of a design and type containing shields, reflectors, fracture panels or recessed light such that the cutoff angle is 90 degrees or less. For purposes herein, the cutoff angle is that angle formed by a line drawn from the direction of light rays at the light source and a line perpendicular to the ground from the light source above which no light is permitted.
(d) Sustainability: The organizing guidance of development which includes four interconnected domains of ecology, economics, politics and culture which are capable of being continued with minimal long-term effect on the environment. For the purposes of this zoning district, all development proposals shall include property owner/developer discretionary mitigation designs to address minimal impacts on the environment through land use, building design and construction, energy use, drainage, air quality, renewable resources, waste disposal, etc.
Sec. 23-5.17.3. – TND GENERAL DESIGN PARAMETERS: NEW DEVELOPMENT
Traditional Neighborhood Development plans shall include the following design parameters for new developments on un-platted (vacant) property:
1. Traditional Neighborhood Development project must include a minimum of thirty (30) acres.
2. Architecture themes for the overall development or for each component section.
3. A center or focal point location which may be a park, square, natural feature, building, clock tower, fountain, statue or other public art piece.
4. Edge features which clearly identify entrances/exits (gateways) with adjacent streets.
5. All buildable lots, irrespective of land use, must front on a public street right-of-way.
6. All residential buildings are encouraged to have a rear private alley access.
7. All buildable lots, irrespective of land use, must be served by underground utilities.
8. All public streets shall include public sidewalks with a minimum seven (7) foot width on both sides of the right-of-way.
9. Street trees shall be designated and required on both sides of each public street irrespective of right-of-way width. Street trees shall be located between the inside edge of the sidewalk and the street curb, except where a front yard exists, the street tree may be placed in a street tree servitude between the outside edge of the sidewalk and lot building.
10. Ten (10%) percent of the TND project geography shall be dedicated for public open space excluding public street right-of-way.
11. Service mail postal delivery for all buildable lots, irrespective of land use, must be centralized at a location within five hundred (500) feet of development project center or focal point location.
12. It is recommended that the community icon be incorporated prominently in the development architecture in one of the following options: street lights, landscape furniture, buildings, public spaces, or gateways.
13. Public streets shall have a minimum thirty (30) foot right-of-way inclusive of street tree planting strips and sidewalks.
14. Signage shall be limited to minimum allowed in Section 23-7.8 of this zoning ordinance.
15. All off-street parking provided for commercial/business/residential land uses shall be located in the rear of buildings on buildable lots.
16. Not more than five (5) percent of the residential units in the TND development may be built or utilized for rental market purposes.
17. The Traditional Neighborhood Development project shall establish and sustain a private development association of property owners with monthly financial assessments (reviewed and assessed annually) sufficient to maintain public spaces and street trees within the development geography.
18. Street lights shall utilize LED (Light Emitting Diodes) and be designed for down-lighting.
19. Residential density must be not less than five (5) units per acre overall, but may vary from street to street within development geography.
20. Development sustainability is a desirable goal for Traditional Neighborhood Development and both public and private infrastructure should have and are encouraged to apply sustainability to the highest degree practical in the project.
21. Not more than twenty (20) percent of the land use within the development may be non-residential at grade level. Vertical structures above the first floor may be unrestricted in use.
22. Community Development District(s) may be required and established for the project subject to the viability of a property owners association.
Sec. 23-5.17.4 – TND RESERVED.
Sec. 23-5.17.5. – TND RESERVED.
Sec. 23-5.17.6. – TND GENERAL DESIGN PARAMETERS – RE-DEVELOPMENT
Traditional Neighborhood Development for revitalization or redevelopment in older established neighborhoods shall include the following design parameters:
1. Traditional Neighborhood Development project must include a minimum of twenty residential or limited mixed use recognized buildable lots
2. Architecture theme or style for overall development.
3. TND Edge Features which clearly identify entrances/exits (gateways) on existing streets.
7. All public streets bordering or included in the TND boundary shall include public sidewalks with a minimum seven (7) foot width on applicable lots.
8. Street trees shall be designated and required on both sides of each public street irrespective of right-of-way width. Street trees shall be located between the inside edge of the banquette and the street curb, except where a front yard exists, the street tree may be placed in a street tree servitude between the outside edge of the banquette and lot building. When only one side of a public street is included in the TND boundary, only the applicable side of the street is required to have street trees and sidewalks.
9. Service mail postal delivery for all buildable lots within the TND district boundary, irrespective of land use, must be centralized at a designated location.
11. Existing public streets shall have a minimum thirty (30) foot right-of-way inclusive of street tree planting strips and sidewalks.
13. All off-street parking provided for commercial/business/residential land uses shall be located in the rear of buildings on approved buildable lots.
15. A Traditional Neighborhood Development for Redevelopment shall include a Community Development District (in accordance with state enabling legislation) approved and adopted by the City of Breaux Bridge Board of Aldermen and effect all buildable lots within the TND development geography.
18. All buildable lots within the development geography of the TND must be contiguous except where separated by a public street.
19. Sustainability is a desirable and primary goal in Traditional Neighborhood Development and both public and private infrastructure should have and are encouraged to identify and utilize sustainability tools, techniques, design and applications to the highest degree practical in the TND district.
21. All existing public streets with TND development properties fronting or adjacent thereto must be identified in the Concept Review Plan and include an evaluation of public infrastructure needs by the City.
22. All structures within the TND shall be planned and designed for permanent installation.
Sec. 23-5.17.9. – GENERAL ZONING REGULATIONS.
General Zoning Regulations not in conflict with Section 23-5.17 through 23-5.17.8 are applicable in the Traditional Neighborhood Development Zoning District.
BE IT FURTHER ORDAINED by the Board of Aldermen for the City of Breaux Bridge, Louisiana, that the provisions of this ordinance are hereby declared to be severable, and if any provision, word, phrase, or clause of this ordinance or the application thereof to any person or circumstance is held invalid, such invalidity shall not affect the validity of the remaining portions thereof.
BE IT FURTHER ORDAINED by the Board of Alderman for the City of Breaux Bridge, Louisiana, duly convened in regular session on the 12th day of November, 2019, that this ordinance shall become effective upon signature of the Mayor of the City of Breaux Bridge, Louisiana, the lapse of ten (10) days after receipt of the Mayor of the City of Breaux Bridge, Louisiana without signature or veto, or upon an override of a veto, whichever occurs first.
UPON MOTION of Ernest "E.J." Ledet, seconded by Neil Melancon, and upon verification and assurance that the foregoing ordinance was:
Upon motion of Neil Melancon, duly seconded by Eddy LeBlanc and unanimously carried, the Board of Aldermen approved the following three names to be submitted for the Retirement Community Oversight Committee. The names are Steve Frey, Dennis Potier and Brandi McKnight.
Upon motion of Ryan Breaux, duly seconded by Eddy LeBlanc and unanimously carried, the Board of Aldermen authorized Mayor Ricky Calais to enter into a Cooperative Endeavor/Intergovernmental Agreement with the Parish Government in regards to abating the tax North of I-10, should the 1% Sales Tax proposed by the City pass on Saturday November 16, 2019.
Upon motion of Ryan Breaux, duly seconded by Eddy LeBlanc and unanimously carried, the Board of Aldermen awarded the bid to M.P. Dumesnil Construction, LLC for the sewer extension project North of I-10.
Upon motion of Neil Melancon, duly seconded by Ernest Ledet and unanimously carried, the meeting was adjourned.
___________________________________________ ______________________________
Kristi LeBlanc, CMC Ricky J. Calais


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Home Directors Brandon Cronenberg
Brandon Cronenberg
B: January 10, 1980 in Toronto, Ontario
The son of the renowned director David Cronenberg, Brandon Cronenberg's first short, Broken Tulips, won Best Director through the enRoute Student Film Festival and the HSBC Filmmaker Award for Best Screenplay. Antiviral, his first feature film, was selected for competition in the Un Certain Regard category at the 2012 Cannes Film Festival and won Best Canadian First Feature at the Toronto International Film Festival that year. His 2020 film, Possessor, is about a corporate agent who uses brain-implant technology to inhabit other people's bodies, driving them to commit assassinations. It was selected to screen in the World Cinema Dramatic Competition at Sundance, where it had its World Premiere.
In March 2021, the Vancouver Film Critics Circle named Brandon Cronenberg Best Canadian Film Director for his work on Possessor.
Broken Tulips (2008, short)
The Camera and Christopher Merk (2010, short)
Please Speak Continuously And Describe Your Experiences As They Come To You (2019, short)
Credits as a Screenwriter:
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