<p>I believe the orbital angular momentum would need to radiate away in gravitational waves as the merger proceeded.  I don't know if any of the spin angular momentum would also radiate away, or if you'd still end up with a maximally rotating black hole.  That's probably an oversimplification, one should be skeptical of anything but a full calculation.  Note, for example, that we would not want to overlook the kinetic energy of the orbit when we calculate the mass-energy of the system, so if some of that mass-energy ends up in the final black hole mass, it might not seem maximally rotating any more.  So although I'm not giving a calculation, I'm saying two things:
1) orbital decay will produce gravitational waves that might carry away angular momentum, and
2) orbital energy counts as mass-energy for the ultimate black hole, so it might not be maximally rotating even if you forget gravitational radiation.</p>

CC BY-SA 3.0
2016-09-19T12:32:16.057Z
I'm pretty sure the angular momentum remains independent from the energy, so you can't really trade angular momentum and energy back and forth; they both have to conserved. But otherwise, yes: excess angular momentum is radiated away as gravitational waves.
Peter Erwin
CC BY-SA 3.0
2016-09-19T15:16:21.457Z
I wasn't saying you trade energy for angular momentum, I was saying the maximum allowed ratio of angular momentum to mass must really be a maximum allowed ratio of angular momentum to energy, including orbital energy.   So you might not have to get rid of as much angular momentum as you might otherwise think.
Ken G
CC BY-SA 3.0
2016-09-19T05:34:09.370Z
2016-09-19T05:34:09.370Z
Ken G
<p>The simple answer is that <strong>no, black holes cannot merge into a new black hole with a spin greater than the maximum allowed spin.</strong> The reason being that such an act would cause the black hole to show us a "<a href="https://en.wikipedia.org/wiki/Naked_singularity" rel="noreferrer">naked singularity</a>". Black holes have an event horizon which shields their singularity from observation by the outside universe. As they spin faster, that event horizon shrinks. At some point, it completely disappears, causing the singularity to become "naked" and observable to the universe. Some believe that naked singularities cannot possibly form, mainly because if they could, causality and physics would break down. This concept is known as the <a href="https://en.wikipedia.org/wiki/Cosmic_censorship_hypothesis" rel="noreferrer">cosmic censorship hypothesis</a>.</p>

<p>I found a statement concerning this matter in <a href="http://rads.stackoverflow.com/amzn/click/052151407X" rel="noreferrer"><em>Numerical Relativity: Solving Einstein's Equations on the Computer</em></a>, which I believe is relevant (emphasis mine).</p>

<blockquote>
  <p>Black hole spins that are aligned with the orbital angular momentum
  increase the binary's total angular momentum. If this total angular
  momentum exceeds the maximum angular momentum of a Kerr black hole,
  then <strong>the binary cannot merge until a sufficient amount of angular
  momentum has been radiated away</strong>. Quite generally, we expect binaries
  with black hole spins aligned with the orbital angular momentum to
  merge more slowly than binaries with spins that are anti-aligned.
  This effect, sometimes <strong>referred to as "orbital hang-up"</strong>, has been
  explored with numerical simulations.</p>
</blockquote>

<p><a href="https://arxiv.org/pdf/gr-qc/0604012v2.pdf" rel="noreferrer">One such numerical simulation</a> looked at aligned and anti-aligned mergers and found that the aligned black holes took much longer to merge and radiated away more energy, in the form of gravitational waves, before they merged.</p>

<p>There is another way to burn off some of that spin angular momentum too. When spinning black holes merge, they experience a "kick" in their linear momentum. In other words, they suddenly speed up in their motion through space. This kick is a result of converting some of the two distinct black holes' orbital and spin momentums into the merged black hole's linear momentum. Quoting the same book as above concerning these kicks:</p>

<blockquote>
  <p>Most of the initial calculations focused on black hole spins that are
  aligned or anti-aligned with the orbital angular momentum. The
  resulting kicks are several hundred km/s in magnitude, easily
  exceeding the maximum kick of approximately 175 km/s found for
  non-spinning black holes.</p>
</blockquote>

<p>In summation, two spinning black holes cannot merge into a black hole which is spinning faster than the maximal rotation. <strong>Gravitational waves and the linear momentum "kick" play an important part in helping binary black holes to lose spin energy, such that the merged black hole doesn't exceed a maximal rotation.</strong></p>

<p>I think the really interesting question that should be asked is, how do two black holes know, before merging, that their merger cannot happen as it would violate the cosmic censorship hypothesis? How do they know they need to radiate away extra energy before they can merge? What is the mechanism that prevents them from merging? Only time can tell for now.</p>

CC BY-SA 3.0
2016-09-19T14:17:00.673Z
2016-09-19T16:20:49.730Z
2016-09-19T16:20:49.730Z
zephyr
<p>The black hole <a href="http://web.archive.org/web/20120507004507/http://www.cosmosmagazine.com/node/873">GRS 1915+105 was observed to be spinning</a> at near the theoretical <a href="http://www.universetoday.com/109308/how-fast-do-black-holes-spin/">maximum spin rate</a>. </p>

<p>Assuming you had two such black holes spinning clockwise, and also orbiting each other clockwise, what would happen if they merged? How could the new black hole avoid breaking the rotational speed limit? Where would the extra angular momentum go?</p>

CC BY-SA 3.0
2016-09-19T13:25:46.543Z
I should say that there's nothing to necessarily restrict a black hole from exceeding the maximum spin rate. The reason we believe black holes don't (or can't) is because it would result in a "naked singularity" which we believe to be impossible. However, aside from never seeing such a thing, nothing suggests it actually is impossible.
zephyr
CC BY-SA 3.0
2016-09-19T13:30:06.837Z
Possibly related: http://physics.stackexchange.com/questions/277073/what-happens-to-the-angular-momentum-of-two-merging-black-holes
zephyr
CC BY-SA 3.0
2016-09-19T22:34:51.030Z
@zephyr thanks! Your answer was so detailed, but your comment implies that it's an open problem. It's very interesting to think how  the black holes could know that the merging system has too much angular momentum. I would never have imagined an answer that said they would slow their merge to radiate off the extra energy. Fascinating!
joseph.hainline
CC BY-SA 3.0
2016-09-20T13:13:35.483Z
It most certainly is an open problem. I think I was just trying to impress upon you the idea that most of the concepts surrounding this topic are still hypothetical. They only exist in equations and physics simulations. We just don't have the observational evidence to actually verify most of it. We only experimentally proved gravitational waves even existed a year ago. In time though, hopefully we'll get a much deeper understanding of black holes.
zephyr
CC BY-SA 3.0
2016-09-20T15:01:49.243Z
@zephyr in the physics simulations, what provides the "friction" that slows down the mergers when angular momentum is too high? What's the physics basis for the "orbital hang-up" idea?
joseph.hainline
CC BY-SA 3.0
2016-09-20T15:05:35.437Z
That's probably a good enough question to be it's own question on here. Alas, you're venturing outside my realm of knowledge. I'd have to do some deep reading to determine that. My guess though, would be that the spin in some way contributes to the orbital motion (likely through frame dragging) and if it is too high, physically prevents the objects from approaching too closely, requiring that some energy be lost first before the black holes are allowed to merge. But again, that's a complete guess so don't take my word for it.
zephyr
<black-hole><rotation>
Could the merger of two rotating black holes create another that breaks the rotational speed limit?
joseph.hainline
# Could the merger of two rotating black holes create another that breaks the rotational speed limit?

(Asked by: username_0 on 2016-09-19)

The black hole [GRS 1915+105 was observed to be spinning](http://web.archive.org/web/20120507004507/http://www.cosmosmagazine.com/node/873) at near the theoretical [maximum spin rate](http://www.universetoday.com/109308/how-fast-do-black-holes-spin/).

Assuming you had two such black holes spinning clockwise, and also orbiting each other clockwise, what would happen if they merged? How could the new black hole avoid breaking the rotational speed limit? Where would the extra angular momentum go?

**Tags:** black-hole, rotation
> **Comments:**
> **username_1**: I should say that there's nothing to necessarily restrict a black hole from exceeding the maximum spin rate. The reason we believe black holes don't (or can't) is because it would result in a "naked singularity" which we believe to be impossible. However, aside from never seeing such a thing, nothing suggests it actually is impossible.  
> **username_1**: Possibly related: http://physics.stackexchange.com/questions/277073/what-happens-to-the-angular-momentum-of-two-merging-black-holes  
> **username_0**: @zephyr thanks! Your answer was so detailed, but your comment implies that it's an open problem. It's very interesting to think how  the black holes could know that the merging system has too much angular momentum. I would never have imagined an answer that said they would slow their merge to radiate off the extra energy. Fascinating!  
> **username_1**: It most certainly is an open problem. I think I was just trying to impress upon you the idea that most of the concepts surrounding this topic are still hypothetical. They only exist in equations and physics simulations. We just don't have the observational evidence to actually verify most of it. We only experimentally proved gravitational waves even existed a year ago. In time though, hopefully we'll get a much deeper understanding of black holes.  
> **username_0**: @zephyr in the physics simulations, what provides the "friction" that slows down the mergers when angular momentum is too high? What's the physics basis for the "orbital hang-up" idea?  
> **username_1**: That's probably a good enough question to be it's own question on here. Alas, you're venturing outside my realm of knowledge. I'd have to do some deep reading to determine that. My guess though, would be that the spin in some way contributes to the orbital motion (likely through frame dragging) and if it is too high, physically prevents the objects from approaching too closely, requiring that some energy be lost first before the black holes are allowed to merge. But again, that's a complete guess so don't take my word for it.  

---

## 2 answers

### Answer by username_1 on 2016-09-19. Score: 10 | Accepted answer

The simple answer is that **no, black holes cannot merge into a new black hole with a spin greater than the maximum allowed spin.** The reason being that such an act would cause the black hole to show us a "[naked singularity](https://en.wikipedia.org/wiki/Naked_singularity)". Black holes have an event horizon which shields their singularity from observation by the outside universe. As they spin faster, that event horizon shrinks. At some point, it completely disappears, causing the singularity to become "naked" and observable to the universe. Some believe that naked singularities cannot possibly form, mainly because if they could, causality and physics would break down. This concept is known as the [cosmic censorship hypothesis](https://en.wikipedia.org/wiki/Cosmic_censorship_hypothesis).

I found a statement concerning this matter in [*Numerical Relativity: Solving Einstein's Equations on the Computer*](http://rads.stackoverflow.com/amzn/click/052151407X), which I believe is relevant (emphasis mine).

> Black hole spins that are aligned with the orbital angular momentum
> increase the binary's total angular momentum. If this total angular
> momentum exceeds the maximum angular momentum of a Kerr black hole,
> then **the binary cannot merge until a sufficient amount of angular
> momentum has been radiated away**. Quite generally, we expect binaries
> with black hole spins aligned with the orbital angular momentum to
> merge more slowly than binaries with spins that are anti-aligned.
> This effect, sometimes **referred to as "orbital hang-up"**, has been
> explored with numerical simulations.

[One such numerical simulation](https://arxiv.org/pdf/gr-qc/0604012v2.pdf) looked at aligned and anti-aligned mergers and found that the aligned black holes took much longer to merge and radiated away more energy, in the form of gravitational waves, before they merged.

There is another way to burn off some of that spin angular momentum too. When spinning black holes merge, they experience a "kick" in their linear momentum. In other words, they suddenly speed up in their motion through space. This kick is a result of converting some of the two distinct black holes' orbital and spin momentums into the merged black hole's linear momentum. Quoting the same book as above concerning these kicks:

> Most of the initial calculations focused on black hole spins that are
> aligned or anti-aligned with the orbital angular momentum. The
> resulting kicks are several hundred km/s in magnitude, easily
> exceeding the maximum kick of approximately 175 km/s found for
> non-spinning black holes.

In summation, two spinning black holes cannot merge into a black hole which is spinning faster than the maximal rotation. **Gravitational waves and the linear momentum "kick" play an important part in helping binary black holes to lose spin energy, such that the merged black hole doesn't exceed a maximal rotation.**

I think the really interesting question that should be asked is, how do two black holes know, before merging, that their merger cannot happen as it would violate the cosmic censorship hypothesis? How do they know they need to radiate away extra energy before they can merge? What is the mechanism that prevents them from merging? Only time can tell for now.


---

### Answer by username_2 on 2016-09-19. Score: 5

I believe the orbital angular momentum would need to radiate away in gravitational waves as the merger proceeded. I don't know if any of the spin angular momentum would also radiate away, or if you'd still end up with a maximally rotating black hole. That's probably an oversimplification, one should be skeptical of anything but a full calculation. Note, for example, that we would not want to overlook the kinetic energy of the orbit when we calculate the mass-energy of the system, so if some of that mass-energy ends up in the final black hole mass, it might not seem maximally rotating any more. So although I'm not giving a calculation, I'm saying two things:
1) orbital decay will produce gravitational waves that might carry away angular momentum, and
2) orbital energy counts as mass-energy for the ultimate black hole, so it might not be maximally rotating even if you forget gravitational radiation.

> **Comments:**
> **username_3**: I'm pretty sure the angular momentum remains independent from the energy, so you can't really trade angular momentum and energy back and forth; they both have to conserved. But otherwise, yes: excess angular momentum is radiated away as gravitational waves.  
> **username_2**: I wasn't saying you trade energy for angular momentum, I was saying the maximum allowed ratio of angular momentum to mass must really be a maximum allowed ratio of angular momentum to energy, including orbital energy.   So you might not have to get rid of as much angular momentum as you might otherwise think.  

---

