<blockquote>
  <p>Can we (theoretically) spin the black hole so strong so it will be broken apart by centrifugal force?</p>
</blockquote>

<p>For a Kerr-Newman (rotating, charged, isolated) black hole of mass $M$, angular momentum $J$, and charge $Q$, the surface area of the event horizon is given by
$$A = 8M\left[M^2 + (M^2-a^2-Q^2)^{1/2} - Q^2/2\right]\text{,}$$
where $a = J/M$. An <em>extremal black hole</em> occurs when $M^2 = a^2 + Q^2$. Beyond that, if the black hole is even more overspun or overcharged, is an "overextremal" Kerr-Newman spacetime, which wouldn't really be a black hole at all, but rather a naked singularity.</p>

<p>Thus, I interpret your question as asking whether or not a black hole can be be spun up to the extremal limit and beyond, so as to destroy the event horizon. It's very probable that it can't be done.</p>

<p>Wald proved in 1974 that as one flings matter into a black hole to try to increase its angular momentum, the nearer to an extremal black hole it is, the harder it is to continue this process: a fast-spinning black hole will repel matter that would take it beyond the extremal limit. There are other schemes, and though I'm not aware of any <em>completely general</em> proof within classical general relativity, the continual failure of schemes like this is well-motivated by the connection between black hole dynamics and thermodynamics.</p>

<p>For example, the Hawking temperature of the black hole is $T_\text{H} = \kappa/2\pi$, where
$$\kappa = \frac{\sqrt{M^2-a^2-Q^2}}{2M\left(M+\sqrt{M^2-a^2-Q^2}\right)-Q^2}$$
is the black hole's surface gravity. Thus, even reaching the extremal limit is thermodynamically equivalent to cooling a system to absolute zero.</p>

CC BY-SA 3.0
2014-05-25T02:12:49.340Z
2014-05-25T02:12:49.340Z
Stan Liou
<p>I don't have all of the math off the top of my head, but from my conceptual understanding, it is not possible.</p>

<p>Black holes have a large enough gravitational attraction that even light cannot escape even from well beyond the "surface" (that is if the black hole has a low enough mass that it still has a surface and has not collapsed into a singularity).  That would mean that it would have to spin fast enough that the surface is moving significantly faster than the speed of light in order to have enough linear momentum (often colloquially called "centrifugal force" in a circular reference frame) to escape, which according to the theory of relativity is not possible.</p>

<p>Hawking radiation is only possible because the electromagnetic radiation is moving very nearly to orthogonally to the "surface" of the black hole and light can only be "bent" by gravity, it can't be pulled to a stop.</p>

CC BY-SA 3.0
2014-05-25T08:44:17.103Z
There are several conceptual problems with this answer. It suggests that the "surface" is something other than the event horizon--then what is it? It suggests that Hawking radiation is limited to massless radiation like electromagnetic--not true. It suggests that black holes can't stop light--the horizon is a lightlike surface that does that.
Stan Liou
CC BY-SA 3.0
2014-05-25T04:38:54.573Z
2014-05-25T04:38:54.573Z
user1738
<p>Black holes can evaporate through a quantum process known as <a href="http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html" rel="nofollow">Hawking Radiation</a> and that's it.</p>

CC BY-SA 3.0
2014-05-24T20:46:56.833Z
2014-05-24T20:46:56.833Z
Jeremy
<p>Let's try the following:</p>

<p>Equate the forces:</p>

<p>$$\begin{eqnarray*}
F_c &amp;=&amp; \frac{mv^2}R\\
F_g &amp;=&amp; \frac{GMm}{R^2}\\
\newline
mv^2/R &amp;=&amp; \frac{GMm}{R^2}\\
v^2 &amp;=&amp; \frac{GM}R
\end{eqnarray*}$$</p>

<p>Since the radius is $R_s = 2GM/c^2$</p>

<p>$$\begin{eqnarray*}
v^2 &amp;=&amp; \frac{GM}{2GM/c^2}\\
v &amp;=&amp; \sqrt{c^2/2}\\
v &amp;=&amp; \frac{c}{\sqrt2}\\
v &amp;=&amp; 0,707c
\end{eqnarray*}$$</p>

<p>I don't know if I made all the considerations, but as far as my knowledge goes, if the blackhole is spinning faster than $0,707c$, the event horizon won't be able to maintain itself on the current radius.</p>

<p>However, when the radius expands, the rotation will slow down by conservation of angular momentum... so I don't think it will rip apart... perhaps become a "grey hole"?</p>

<p>Please forgive me if any fundamental mistake was made, I'm new to all this... :P</p>

CC BY-SA 3.0
2015-06-03T20:11:25.763Z
I like the term "Grey hole".
userLTK
CC BY-SA 3.0
2017-10-05T15:10:10.793Z
This is an old answer, but I thought I'd drop this here because it addresses orbital velocity of black holes.   you'd need to have the theoretical edge of the black hole at the event horizon spinning at C to escape, which is obviously impossible.   https://physics.stackexchange.com/questions/207816/what-is-the-relation-between-orbital-velocity-and-escape-velocity-in-strongly-re
userLTK
CC BY-SA 3.0
2014-10-07T14:32:04.543Z
This looks Newtonian. Did you consider the curvature of spacetime near a Black Hole? See also "Kerr solution" for Black Holes.
Gerald
CC BY-SA 3.0
2014-10-07T11:36:24.107Z
2014-10-07T15:02:07.043Z
2014-10-07T15:02:07.043Z
Matheus Dardenne
<p>Interesting. This process could impact the black hole formation in the first place. Consider a rotating star that dies and starts to shrink due to gravitational forces. As it shrinks, all its mass will be more and more compacted in a smaller radius. This will have two consequences: 1) the gravitational force atracting different parts of the body will will grow up with the inverse of squared radius and 2) its rotational speed will increase due to angular momentum conservation and the expanding force, due to the rotation, will grow up with the inverse of radius cubed. This means the expanding force will grow more quickly than the contracting one and, at least in Newtonian view, the expanding force will win. From this point of view, it looks like a rotating star would never form a black hole... </p>

CC BY-SA 3.0
2017-10-05T16:21:20.990Z
You might like this article.   http://www.slate.com/blogs/quora/2014/02/10/if_a_coin_sized_black_hole_were_placed_at_earth_s_center_what_would_happen.html
userLTK
CC BY-SA 3.0
2017-10-05T10:41:48.463Z
2017-10-05T10:41:48.463Z
mmicoski
<p>As far as we know there is nothing that can stop a black hole. For this notion to make sense you must first look at what is currently known about <a href="http://en.wikipedia.org/wiki/Black_hole" rel="nofollow noreferrer">black holes</a>. Once you get a grasp of it, then you will see that due to our current understanding of the Cosmos there is nothing we can do to black holes. </p>

<p>It is true that Hawking Radiation can affect a black hole, but that is only for very very small black holes.</p>

<p>By the way, in Physics there is no centrifugal force -- this is actually a misconception many people have. However, there is <a href="http://en.wikipedia.org/wiki/Centripetal_force" rel="nofollow noreferrer">centripetal force</a>. </p>

<p><img src="https://i.sstatic.net/WlSJS.jpg" alt="enter image description here"></p>

CC BY-SA 3.0
2015-06-03T19:48:55.160Z
This "answer" is pretty vague, makes questionable statements, and has no real bearing on the original query.
Florin Andrei
CC BY-SA 3.0
2014-05-24T21:41:23.063Z
Obligatory rebuttal-via-xkcd link: http://xkcd.com/123/
Ilmari Karonen
CC BY-SA 3.0
2014-05-24T22:01:13.030Z
@IlmariKaronen Thanks for the down-vote, however, you do realize that the cartoon doesn't prove anything right? There is a difference between Centripetal force and centrifugal.
axwcode
CC BY-SA 3.0
2014-05-26T03:54:56.337Z
To be fair, the cartoon points out that centrifugal force is as inertial force, which is true. Arguably it's sensible to interpret inertial forces as "not real", but I'm not sure what bearing that has on this question, since gravitational force is an inertial force as well.
Stan Liou
CC BY-SA 3.0
2014-05-24T20:41:05.597Z
2014-05-24T20:46:15.653Z
2014-05-24T20:46:15.653Z
axwcode
<p>I can't imagine the forces involved in black holes' lives. So please, help me to find out, if it is possible or not to destroy black hole in this specific way.</p>

CC BY-SA 3.0
2014-05-25T00:50:57.010Z
I am not sure, but I think that in order to increase its spin efficiently, you need to throw stuff at it, and if you do you will also increase its mass; in the strong field limit of GR, the corresponding mass increase prevents centrifugal force from breaking it apart. At best it becomes a Kerr black hole with 'a' asymptotically close to 1. For black holes, gravity always win! (if you want to torque it up without throwing things, you ll have to be fairly far away and it won't be very efficient)
chris
<black-hole>
Can we (theoretically) spin the black hole so strong that it will be broken apart by centrifugal force?
Pavel Voronin
# Can we (theoretically) spin the black hole so strong that it will be broken apart by centrifugal force?

(Asked by: username_0 on 2014-05-24)

I can't imagine the forces involved in black holes' lives. So please, help me to find out, if it is possible or not to destroy black hole in this specific way.

**Tags:** black-hole
> **Comments:**
> **username_1**: I am not sure, but I think that in order to increase its spin efficiently, you need to throw stuff at it, and if you do you will also increase its mass; in the strong field limit of GR, the corresponding mass increase prevents centrifugal force from breaking it apart. At best it becomes a Kerr black hole with 'a' asymptotically close to 1. For black holes, gravity always win! (if you want to torque it up without throwing things, you ll have to be fairly far away and it won't be very efficient)  

---

## 6 answers

### Answer by username_2 on 2014-05-25. Score: 23

> Can we (theoretically) spin the black hole so strong so it will be broken apart by centrifugal force?

For a Kerr-Newman (rotating, charged, isolated) black hole of mass $M$, angular momentum $J$, and charge $Q$, the surface area of the event horizon is given by
$$A = 8M\left[M^2 + (M^2-a^2-Q^2)^{1/2} - Q^2/2\right]\text{,}$$
where $a = J/M$. An *extremal black hole* occurs when $M^2 = a^2 + Q^2$. Beyond that, if the black hole is even more overspun or overcharged, is an "overextremal" Kerr-Newman spacetime, which wouldn't really be a black hole at all, but rather a naked singularity.

Thus, I interpret your question as asking whether or not a black hole can be be spun up to the extremal limit and beyond, so as to destroy the event horizon. It's very probable that it can't be done.

Wald proved in 1974 that as one flings matter into a black hole to try to increase its angular momentum, the nearer to an extremal black hole it is, the harder it is to continue this process: a fast-spinning black hole will repel matter that would take it beyond the extremal limit. There are other schemes, and though I'm not aware of any *completely general* proof within classical general relativity, the continual failure of schemes like this is well-motivated by the connection between black hole dynamics and thermodynamics.

For example, the Hawking temperature of the black hole is $T\_\text{H} = \kappa/2\pi$, where
$$\kappa = \frac{\sqrt{M^2-a^2-Q^2}}{2M\left(M+\sqrt{M^2-a^2-Q^2}\right)-Q^2}$$
is the black hole's surface gravity. Thus, even reaching the extremal limit is thermodynamically equivalent to cooling a system to absolute zero.


---

### Answer by username_3 on 2014-05-25. Score: 2

I don't have all of the math off the top of my head, but from my conceptual understanding, it is not possible.

Black holes have a large enough gravitational attraction that even light cannot escape even from well beyond the "surface" (that is if the black hole has a low enough mass that it still has a surface and has not collapsed into a singularity). That would mean that it would have to spin fast enough that the surface is moving significantly faster than the speed of light in order to have enough linear momentum (often colloquially called "centrifugal force" in a circular reference frame) to escape, which according to the theory of relativity is not possible.

Hawking radiation is only possible because the electromagnetic radiation is moving very nearly to orthogonally to the "surface" of the black hole and light can only be "bent" by gravity, it can't be pulled to a stop.

> **Comments:**
> **username_2**: There are several conceptual problems with this answer. It suggests that the "surface" is something other than the event horizon--then what is it? It suggests that Hawking radiation is limited to massless radiation like electromagnetic--not true. It suggests that black holes can't stop light--the horizon is a lightlike surface that does that.  

---

### Answer by username_4 on 2014-05-24. Score: 1

Black holes can evaporate through a quantum process known as [Hawking Radiation](http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html) and that's it.


---

### Answer by username_8 on 2017-10-05. Score: 0

Interesting. This process could impact the black hole formation in the first place. Consider a rotating star that dies and starts to shrink due to gravitational forces. As it shrinks, all its mass will be more and more compacted in a smaller radius. This will have two consequences: 1) the gravitational force atracting different parts of the body will will grow up with the inverse of squared radius and 2) its rotational speed will increase due to angular momentum conservation and the expanding force, due to the rotation, will grow up with the inverse of radius cubed. This means the expanding force will grow more quickly than the contracting one and, at least in Newtonian view, the expanding force will win. From this point of view, it looks like a rotating star would never form a black hole...

> **Comments:**
> **username_6**: You might like this article.   http://www.slate.com/blogs/quora/2014/02/10/if_a_coin_sized_black_hole_were_placed_at_earth_s_center_what_would_happen.html  

---

### Answer by username_9 on 2014-05-24. Score: 0

As far as we know there is nothing that can stop a black hole. For this notion to make sense you must first look at what is currently known about [black holes](http://en.wikipedia.org/wiki/Black_hole). Once you get a grasp of it, then you will see that due to our current understanding of the Cosmos there is nothing we can do to black holes.

It is true that Hawking Radiation can affect a black hole, but that is only for very very small black holes.

By the way, in Physics there is no centrifugal force -- this is actually a misconception many people have. However, there is [centripetal force](http://en.wikipedia.org/wiki/Centripetal_force).

![enter image description here](https://i.sstatic.net/WlSJS.jpg)

> **Comments:**
> **username_11**: Obligatory rebuttal-via-xkcd link: http://xkcd.com/123/  
> **username_9**: @IlmariKaronen Thanks for the down-vote, however, you do realize that the cartoon doesn't prove anything right? There is a difference between Centripetal force and centrifugal.  
> **username_2**: To be fair, the cartoon points out that centrifugal force is as inertial force, which is true. Arguably it's sensible to interpret inertial forces as "not real", but I'm not sure what bearing that has on this question, since gravitational force is an inertial force as well.  
> **username_10**: This "answer" is pretty vague, makes questionable statements, and has no real bearing on the original query.  

---

### Answer by username_5 on 2014-10-07. Score: -1

Let's try the following:

Equate the forces:

$$\begin{eqnarray\*}
F\_c &=& \frac{mv^2}R\\
F\_g &=& \frac{GMm}{R^2}\\
\newline
mv^2/R &=& \frac{GMm}{R^2}\\
v^2 &=& \frac{GM}R
\end{eqnarray\*}$$

Since the radius is $R\_s = 2GM/c^2$

$$\begin{eqnarray\*}
v^2 &=& \frac{GM}{2GM/c^2}\\
v &=& \sqrt{c^2/2}\\
v &=& \frac{c}{\sqrt2}\\
v &=& 0,707c
\end{eqnarray\*}$$

I don't know if I made all the considerations, but as far as my knowledge goes, if the blackhole is spinning faster than $0,707c$, the event horizon won't be able to maintain itself on the current radius.

However, when the radius expands, the rotation will slow down by conservation of angular momentum... so I don't think it will rip apart... perhaps become a "grey hole"?

Please forgive me if any fundamental mistake was made, I'm new to all this... :P

> **Comments:**
> **username_7**: This looks Newtonian. Did you consider the curvature of spacetime near a Black Hole? See also "Kerr solution" for Black Holes.  
> **username_6**: I like the term "Grey hole".  
> **username_6**: This is an old answer, but I thought I'd drop this here because it addresses orbital velocity of black holes.   you'd need to have the theoretical edge of the black hole at the event horizon spinning at C to escape, which is obviously impossible.   https://physics.stackexchange.com/questions/207816/what-is-the-relation-between-orbital-velocity-and-escape-velocity-in-strongly-re  

---

