<p>Any asymmetry would disappear extremely rapidly, damped by the emission of gravitational waves. This is demonstrated by the briefness of the <a href="https://en.wikipedia.org/wiki/Binary_black_hole#Ringdown" rel="nofollow noreferrer">ring-down phase</a> after a binary black hole merger - which is about as extreme an asymmetric accretion event as you could imagine. The outcome of the merger is an axisymmetric, but not spherically symmetric,  Kerr black hole.</p>

CC BY-SA 4.0
2022-02-26T17:51:14.873Z
2022-02-26T17:51:14.873Z
ProfRob
<p>There are two classes of black hole asymmetries I will consider in this answer.  The first the is <a href="https://en.wikipedia.org/w/index.php?title=Kerr_metric&amp;oldid=1069990274" rel="nofollow noreferrer">Kerr</a> black hole which is the class of black holes with non-zero angular momentum and no net charge.  These black holes have a <a href="https://en.wikipedia.org/w/index.php?title=Kerr_metric&amp;oldid=1069990274#Important_surfaces" rel="nofollow noreferrer">non-spherical event horizon</a>, and therefore do not have spherical symmetric, but they do have rotational symmetry about their axis.  This is a steady-state configuration and will persist unless perturbed.</p>
<p><a href="https://i.sstatic.net/K1bygl.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/K1bygl.png" alt="Event horizons and ergospheres of a rotating black hole" /></a><br/>
Image from <a href="https://en.wikipedia.org/wiki/File:Kerr-surfaces.png" rel="nofollow noreferrer">Wikipedia</a>.<br/></p>
<p>The second case considered is a non-steady state such as might be found during the merger of two black holes or another compact object such as a neutron star.  These effects will also occur when any matter enters the black holes, as it will be non-steady-state, but the magnitude of the effects will be smaller.</p>
<p><strong>Prior to the Merger</strong><br/>
Prior to merging, black holes can be deformed by tidal effects.  This does not seem to be a general effect, but only impacts black holes that were not spherical to begin with.</p>
<blockquote>
<p>Through new theoretical analysis, Le Tiec and Casals predict that
tidal bulges can indeed occur during mergers. For a black hole
spinning at 10% of its maximum possible rate in an asymmetric tidal
field, their calculations show that tidal bulges can appear, with a
corresponding quadrupolar TLN of 0.002. In comparison, the quadrupolar
tidal <a href="https://en.wikipedia.org/w/index.php?title=Love_number&amp;oldid=1072334680" rel="nofollow noreferrer">Love numbers</a> (TLN) for a much more deformable Earth is 0.3, while a neutron star has a number of about 0.1. (<a href="https://physicsworld.com/a/spinning-black-holes-can-be-deformed-by-tidal-forces-calculations-reveal/" rel="nofollow noreferrer">Spinning black holes can be deformed by tidal forces, calculations reveal</a>)</p>
</blockquote>
<p>Are also <a href="https://www.ias.edu/video/tidal-deformation-and-dissipation-rotating-black-holes" rel="nofollow noreferrer">Tidal Deformation and Dissipation of Rotating Black Holes</a> (<a href="https://www.ggi.infn.it/talkfiles/slides/slides5313.pdf" rel="nofollow noreferrer">slides</a>).</p>
<p><strong>During the Merger</strong><br/>
During a black hole merger the shape of the event horizon can be come quite complex.</p>
<blockquote>
<p>As two black holes approach each other, a 'duckbill' shape protrudes
from each of the two event horizons towards the other one. This
protrusion extends longer and narrower until it meets the protrusion
from the other black hole. At this point in time the event horizon has
a very narrow X-shape at the meeting point. The protrusions are drawn
out into a thin thread. The meeting point expands to a roughly
cylindrical connection called a bridge. (<a href="https://en.wikipedia.org/w/index.php?title=Binary_black_hole&amp;oldid=1065110756#Shape" rel="nofollow noreferrer">Wikipedia</a>)</p>
</blockquote>
<p><a href="https://i.sstatic.net/x9wFRm.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/x9wFRm.png" alt="enter image description here" /></a><br/>
Image from <a href="https://arxiv.org/abs/1110.1668" rel="nofollow noreferrer">On Toroidal Horizons in Binary Black Hole Inspirals</a><br/></p>
<p>See also <a href="https://astronomy.stackexchange.com/questions/31989/are-black-holes-spherical-during-merger">Are black holes spherical during merger?</a> (as mentioned by <a href="https://astronomy.stackexchange.com/users/7982/uhoh">uhoh</a> in the comments)<br/></p>
<p><strong>After the Merger</strong><br/>
Post merge, the event horizon transitions from a complex state to the steady state Kerr configuration by exiting gravitational waves.</p>
<blockquote>
<p>The merger of a binary black hole gives birth to a highly distorted
final black hole. The gravitational radiation emitted as this black
hole relaxes presents us with the unique opportunity to probe extreme
gravity and its connection with the dynamics of the black hole
horizon.... Once the BHs merge, a highly distorted BH settles into a Kerr BH radiating exponentially decaying ringdown emission. (<a href="https://www.nature.com/articles/s42005-020-00446-7" rel="nofollow noreferrer">Post-merger chirps from binary black holes as probes of the final black-hole horizon</a>)</p>
</blockquote>
<p>See also <a href="https://physics.stackexchange.com/questions/523771/what-causes-a-black-hole-ringdown-and-why-can-it-prove-the-no-hair-theorem">What causes a black hole ringdown and why can it prove the no-hair theorem?</a><br/></p>

CC BY-SA 4.0
2022-02-26T02:59:51.637Z
2022-02-26T02:59:51.637Z
GrapefruitIsAwesome
<p>The only black hole with an isotropic gravitational field around it is the Schwarzschild black hole, but astrophysical black holes have spin angular momentum and thus are instead better modeled by the Kerr black hole. The Kerr black hole spacetime is axisymmetric, i.e., cylindrically symmetric, about its spin axis. The region that surrounds a Kerr black hole is known as the <a href="https://en.wikipedia.org/wiki/Ergosphere" rel="nofollow noreferrer">ergosphere</a>, which is poorly named because it's not spherical for arbitrary spin, and instead is like an oblate spheroid for modest spin and more like a pumpkin for high spin. <a href="https://en.wikipedia.org/wiki/Penrose_process" rel="nofollow noreferrer">Essentially, the ergosphere is</a> &quot;a region of spacetime around the black hole dragged by its rotation faster than the speed of light, meaning that from the point of an outside observer any matter inside is forced to move in the direction of the rotation of the black hole.&quot; A Kerr black hole <a href="https://en.wikipedia.org/wiki/Kerr_metric#Important_surfaces" rel="nofollow noreferrer">has several important surfaces</a>, compared to the simpler Schw case. The ergosphere is bound between the outer event horizon and the outer surface of infinite redshift.</p>
<blockquote>
<p>From an outside observer, if matter falls into a black holes from only one side, would the black hole's growth be asymmetric, and would it's gravity be non-isotropic?</p>
</blockquote>
<p>You seem to be asking about the effect of accretion. In principle, an accretion disk forms around the black hole, so that it accretes matter from the <a href="https://en.wikipedia.org/wiki/Innermost_stable_circular_orbit" rel="nofollow noreferrer">inner-most stable-circular orbit</a> which is beyond the event horizon.</p>
<p>I am not sure what you mean by &quot;would the black hole's growth be asymmetric?&quot; Are you asking about the change to its <a href="https://skyandtelescope.org/astronomy-news/the-appearance-of-a-black-holes-shadow/" rel="nofollow noreferrer">shadow</a> perhaps? In the case of the supermassive black hole at the center of galaxy M87 that was imaged by the Event Horizon Telescope, the shadow <a href="https://iopscience.iop.org/article/10.3847/2041-8213/ab1141" rel="nofollow noreferrer">deviates from circularity within 10%</a>, <a href="https://physics.stackexchange.com/a/472444/201856">consistent with prediction of General Relativity</a> for Kerr black holes. The <a href="https://astronomy.stackexchange.com/questions/30343/why-are-there-uneven-bright-areas-in-this-photo-of-black-hole">asymmetry in the accretion disk</a> is essentially due to relativistic beaming. The <a href="https://iopscience.iop.org/article/10.3847/2041-8213/ab518c" rel="nofollow noreferrer">shadow of a Schw</a> black hole is circular. This implies that an initially non-rotating black hole that begins accreting will start with a circular shadow but will begin to appear as non-circular, as its spin increases, to far away observers. If you're wondering about the ergosphere, as a Kerr black hole accretes, its spin increases, which makes the ergosphere more pumpkin shaped as the outer surface of infinite redshift widens at the equator but is squished at the poles. <a href="https://en.wikipedia.org/wiki/File:Kerr.black.hole.shadow.and.horizons.gif" rel="nofollow noreferrer">This wonderful animation</a> from the wiki page for Kerr black holes shows how the ergosphere depends on the black hole's spin, and how the non-circularity of the black hole's shadow increases with spin.</p>
<p>Some hydrodynamical models consider asymmetric Bondi-Hoyle accretion onto a Schw black hole, but as far as I can tell, it is often assumed that the gas is treated as a test fluid and does not effect the spacetime geometry, implying that the gravitational field around the black hole remains isotropic, for example <a href="https://academic.oup.com/mnras/article/429/4/3144/1013819" rel="nofollow noreferrer">here</a>. In principle, accretion should increase the spin of an initially non-rotating black hole, and thus would remove the isotropy of its surrounding gravitational field, resulting in the Kerr geometry. In models that consider asymmetric accretion onto a Kerr black hole, things are even more complicated. But in principle, the axisymmetry of the Kerr spacetime is preserved as the spin and mass increase due to accretion. This is an area of research for magnetohydrodynamical numerical studies of accretion in the Kerr spacetime.</p>

CC BY-SA 4.0
2022-02-26T11:07:33.083Z
2022-02-26T11:14:31.037Z
2022-02-26T11:14:31.037Z
Daddy Kropotkin
<p>From an outside observer, if matter falls into a black holes from only one side, would the black hole's growth be asymmetric, and would it's gravity be non-isotropic?</p>

CC BY-SA 4.0
2022-02-25T08:47:53.483Z
My uneducated guess is that if you dumped a *huge and continuous stream of matter* into one side of a non-rotating black hole so that it was in a non-equilibrium state for an extended period of time, the event horizon would have a static *ever so slightly non-spherical* shape. Related: [Are black holes spherical during merger?](https://astronomy.stackexchange.com/q/31989/7982) and [What can be learned from, or noted in this LIGO Orrery video?](https://astronomy.stackexchange.com/q/28610/7982)
uhoh
CC BY-SA 4.0
2022-02-25T09:45:09.480Z
Why do you think it might become asymmetric? Is your black hole spinning? Bear in mind that the black hole can move, so it will be gravitationally attracted towards the incoming mass, but it will also obey conservation of momentum when it absorbs that mass.
PM 2Ring
CC BY-SA 4.0
2022-02-25T12:40:05.993Z
@PM2Ring For simplicity sake, let's assume a non-spinning black hole whose matter  is falling in straight center. All of the matter is falling in from one side.
H2Forge
CC BY-SA 4.0
2022-02-25T14:54:24.603Z
It's not going to stay asymmetric for long due to gravitational radiation.
GrapefruitIsAwesome
CC BY-SA 4.0
2022-02-25T16:58:18.633Z
@GrapefruitIsAwesome Could you elaborate or link to an answer?
H2Forge
CC BY-SA 4.0
2022-02-25T16:59:37.937Z
@H2Forge I don't know of one off the top of my head.  If I have a chance to get to it before someone else posts an answer I'll add one.
GrapefruitIsAwesome
<black-hole>
Are asymmetric black holes possible?
H2Forge
# Are asymmetric black holes possible?

(Asked by: username_0 on 2022-02-25)

From an outside observer, if matter falls into a black holes from only one side, would the black hole's growth be asymmetric, and would it's gravity be non-isotropic?

**Tags:** black-hole
> **Comments:**
> **username_1**: My uneducated guess is that if you dumped a *huge and continuous stream of matter* into one side of a non-rotating black hole so that it was in a non-equilibrium state for an extended period of time, the event horizon would have a static *ever so slightly non-spherical* shape. Related: [Are black holes spherical during merger?](https://astronomy.stackexchange.com/q/31989/7982) and [What can be learned from, or noted in this LIGO Orrery video?](https://astronomy.stackexchange.com/q/28610/7982)  
> **username_2**: Why do you think it might become asymmetric? Is your black hole spinning? Bear in mind that the black hole can move, so it will be gravitationally attracted towards the incoming mass, but it will also obey conservation of momentum when it absorbs that mass.  
> **username_0**: @PM2Ring For simplicity sake, let's assume a non-spinning black hole whose matter  is falling in straight center. All of the matter is falling in from one side.  
> **username_3**: It's not going to stay asymmetric for long due to gravitational radiation.  
> **username_0**: @GrapefruitIsAwesome Could you elaborate or link to an answer?  
> **username_3**: @H2Forge I don't know of one off the top of my head.  If I have a chance to get to it before someone else posts an answer I'll add one.  

---

## 3 answers

### Answer by username_4 on 2022-02-26. Score: 4

Any asymmetry would disappear extremely rapidly, damped by the emission of gravitational waves. This is demonstrated by the briefness of the [ring-down phase](https://en.wikipedia.org/wiki/Binary_black_hole#Ringdown) after a binary black hole merger - which is about as extreme an asymmetric accretion event as you could imagine. The outcome of the merger is an axisymmetric, but not spherically symmetric, Kerr black hole.


---

### Answer by username_3 on 2022-02-26. Score: 3

There are two classes of black hole asymmetries I will consider in this answer. The first the is [Kerr](https://en.wikipedia.org/w/index.php?title=Kerr_metric&oldid=1069990274) black hole which is the class of black holes with non-zero angular momentum and no net charge. These black holes have a [non-spherical event horizon](https://en.wikipedia.org/w/index.php?title=Kerr_metric&oldid=1069990274#Important_surfaces), and therefore do not have spherical symmetric, but they do have rotational symmetry about their axis. This is a steady-state configuration and will persist unless perturbed.

[![Event horizons and ergospheres of a rotating black hole](https://i.sstatic.net/K1bygl.png)](https://i.sstatic.net/K1bygl.png)  
Image from [Wikipedia](https://en.wikipedia.org/wiki/File:Kerr-surfaces.png).

The second case considered is a non-steady state such as might be found during the merger of two black holes or another compact object such as a neutron star. These effects will also occur when any matter enters the black holes, as it will be non-steady-state, but the magnitude of the effects will be smaller.

**Prior to the Merger**  
Prior to merging, black holes can be deformed by tidal effects. This does not seem to be a general effect, but only impacts black holes that were not spherical to begin with.

> Through new theoretical analysis, Le Tiec and Casals predict that
> tidal bulges can indeed occur during mergers. For a black hole
> spinning at 10% of its maximum possible rate in an asymmetric tidal
> field, their calculations show that tidal bulges can appear, with a
> corresponding quadrupolar TLN of 0.002. In comparison, the quadrupolar
> tidal [Love numbers](https://en.wikipedia.org/w/index.php?title=Love_number&oldid=1072334680) (TLN) for a much more deformable Earth is 0.3, while a neutron star has a number of about 0.1. ([Spinning black holes can be deformed by tidal forces, calculations reveal](https://physicsworld.com/a/spinning-black-holes-can-be-deformed-by-tidal-forces-calculations-reveal/))

Are also [Tidal Deformation and Dissipation of Rotating Black Holes](https://www.ias.edu/video/tidal-deformation-and-dissipation-rotating-black-holes) ([slides](https://www.ggi.infn.it/talkfiles/slides/slides5313.pdf)).

**During the Merger**  
During a black hole merger the shape of the event horizon can be come quite complex.

> As two black holes approach each other, a 'duckbill' shape protrudes
> from each of the two event horizons towards the other one. This
> protrusion extends longer and narrower until it meets the protrusion
> from the other black hole. At this point in time the event horizon has
> a very narrow X-shape at the meeting point. The protrusions are drawn
> out into a thin thread. The meeting point expands to a roughly
> cylindrical connection called a bridge. ([Wikipedia](https://en.wikipedia.org/w/index.php?title=Binary_black_hole&oldid=1065110756#Shape))

[![enter image description here](https://i.sstatic.net/x9wFRm.png)](https://i.sstatic.net/x9wFRm.png)  
Image from [On Toroidal Horizons in Binary Black Hole Inspirals](https://arxiv.org/abs/1110.1668)

See also [Are black holes spherical during merger?](https://astronomy.stackexchange.com/questions/31989/are-black-holes-spherical-during-merger) (as mentioned by [uhoh](https://astronomy.stackexchange.com/users/7982/uhoh) in the comments)

**After the Merger**  
Post merge, the event horizon transitions from a complex state to the steady state Kerr configuration by exiting gravitational waves.

> The merger of a binary black hole gives birth to a highly distorted
> final black hole. The gravitational radiation emitted as this black
> hole relaxes presents us with the unique opportunity to probe extreme
> gravity and its connection with the dynamics of the black hole
> horizon.... Once the BHs merge, a highly distorted BH settles into a Kerr BH radiating exponentially decaying ringdown emission. ([Post-merger chirps from binary black holes as probes of the final black-hole horizon](https://www.nature.com/articles/s42005-020-00446-7))

See also [What causes a black hole ringdown and why can it prove the no-hair theorem?](https://physics.stackexchange.com/questions/523771/what-causes-a-black-hole-ringdown-and-why-can-it-prove-the-no-hair-theorem)


---

### Answer by username_5 on 2022-02-26. Score: 2

The only black hole with an isotropic gravitational field around it is the Schwarzschild black hole, but astrophysical black holes have spin angular momentum and thus are instead better modeled by the Kerr black hole. The Kerr black hole spacetime is axisymmetric, i.e., cylindrically symmetric, about its spin axis. The region that surrounds a Kerr black hole is known as the [ergosphere](https://en.wikipedia.org/wiki/Ergosphere), which is poorly named because it's not spherical for arbitrary spin, and instead is like an oblate spheroid for modest spin and more like a pumpkin for high spin. [Essentially, the ergosphere is](https://en.wikipedia.org/wiki/Penrose_process) "a region of spacetime around the black hole dragged by its rotation faster than the speed of light, meaning that from the point of an outside observer any matter inside is forced to move in the direction of the rotation of the black hole." A Kerr black hole [has several important surfaces](https://en.wikipedia.org/wiki/Kerr_metric#Important_surfaces), compared to the simpler Schw case. The ergosphere is bound between the outer event horizon and the outer surface of infinite redshift.

> From an outside observer, if matter falls into a black holes from only one side, would the black hole's growth be asymmetric, and would it's gravity be non-isotropic?

You seem to be asking about the effect of accretion. In principle, an accretion disk forms around the black hole, so that it accretes matter from the [inner-most stable-circular orbit](https://en.wikipedia.org/wiki/Innermost_stable_circular_orbit) which is beyond the event horizon.

I am not sure what you mean by "would the black hole's growth be asymmetric?" Are you asking about the change to its [shadow](https://skyandtelescope.org/astronomy-news/the-appearance-of-a-black-holes-shadow/) perhaps? In the case of the supermassive black hole at the center of galaxy M87 that was imaged by the Event Horizon Telescope, the shadow [deviates from circularity within 10%](https://iopscience.iop.org/article/10.3847/2041-8213/ab1141), [consistent with prediction of General Relativity](https://physics.stackexchange.com/a/472444/201856) for Kerr black holes. The [asymmetry in the accretion disk](https://astronomy.stackexchange.com/questions/30343/why-are-there-uneven-bright-areas-in-this-photo-of-black-hole) is essentially due to relativistic beaming. The [shadow of a Schw](https://iopscience.iop.org/article/10.3847/2041-8213/ab518c) black hole is circular. This implies that an initially non-rotating black hole that begins accreting will start with a circular shadow but will begin to appear as non-circular, as its spin increases, to far away observers. If you're wondering about the ergosphere, as a Kerr black hole accretes, its spin increases, which makes the ergosphere more pumpkin shaped as the outer surface of infinite redshift widens at the equator but is squished at the poles. [This wonderful animation](https://en.wikipedia.org/wiki/File:Kerr.black.hole.shadow.and.horizons.gif) from the wiki page for Kerr black holes shows how the ergosphere depends on the black hole's spin, and how the non-circularity of the black hole's shadow increases with spin.

Some hydrodynamical models consider asymmetric Bondi-Hoyle accretion onto a Schw black hole, but as far as I can tell, it is often assumed that the gas is treated as a test fluid and does not effect the spacetime geometry, implying that the gravitational field around the black hole remains isotropic, for example [here](https://academic.oup.com/mnras/article/429/4/3144/1013819). In principle, accretion should increase the spin of an initially non-rotating black hole, and thus would remove the isotropy of its surrounding gravitational field, resulting in the Kerr geometry. In models that consider asymmetric accretion onto a Kerr black hole, things are even more complicated. But in principle, the axisymmetry of the Kerr spacetime is preserved as the spin and mass increase due to accretion. This is an area of research for magnetohydrodynamical numerical studies of accretion in the Kerr spacetime.


---

