<p>First off blackholes can orbit eachother, we can and have proven that because of the amence energy in the form of gravitational waves they give off which we can measure here on earth. </p>

<p>It's possible that the ergosphere would prolong the mergetion of the two blackholes if they have the correct spin corresponding to the (very unlikely) orbit of the other black hole, although it would almost inevitable fall into one of the event horizons eventually because of the gravitational waves it produces. Which gives off a masive amount of kenetic energy. For the blackhole to gain kenetic energy it would have to overcome this energy loss.</p>

CC BY-SA 4.0
2019-01-16T14:19:39.343Z
2019-01-16T20:43:08.147Z
2019-01-16T20:43:08.147Z
Das Stein
<p>Black holes can orbit each other (we know this from the gravitational waves from their eventual mergers) and there is no particular reason against a small black hole passing through the ergosphere of a large black hole. </p>

<p>The main problem is avoiding a merger. The the two-black hole spacetime has no analytic solution and numeric simulations are messy, but a merger will definitely happen if the event horizons overlap. In any case, a rotating black hole has an ergosphere with an equatorial radius of $2GM/c^2$ and event horizon somewhere between this and the limiting radius $GM/c^2$. If we use the extremal case, then we can presumably just barely fit in nearly an identical mass and rotation black hole in the ergosphere. More likely a much smaller black hole could fit in. The direction of rotation <em>would</em> matter for the dynamics, since counter-rotating black holes would tend to coalesce (see <a href="https://duetosymmetry.com/tool/kerr-calculator-v2/" rel="noreferrer">this page</a> for a plot of the relevant radii and where the <a href="https://en.wikipedia.org/wiki/Innermost_stable_circular_orbit" rel="noreferrer">innermost stable circular orbits</a> are). </p>

<p>A single black hole passing through the ergoregion would not be able to perform the Penrose process, but we can imagine a binary black hole pair that is ripped apart by tidal forces and then presumably the remaining hole would be ejected with a lot of energy. So, yes, we could get fast small black holes this way. </p>

<p>In practice this system would lose a lot of energy through gravitational waves, making it likely that the holes would coalesce anyway. The exact limits require numerical relativity simulations to estimate, and this one would be a tough one.</p>

<p>(Note that the gravitational waves also carry away energy, up to 1/8 of the total mass of two equal-sized holes merging, but this energy is very hard to capture. Penrose did note in his classic paper that Misner was first in proposing black hole mining using a variant of this.)</p>

CC BY-SA 3.0
2018-04-27T18:11:36.393Z
2018-04-27T18:11:36.393Z
Anders Sandberg
<p>I recently watched this video on black holes:
<a href="https://www.youtube.com/watch?v=ulCdoCfw-bY" rel="noreferrer">https://www.youtube.com/watch?v=ulCdoCfw-bY</a></p>

<p>And that statement should give you an idea of my level of understanding :)</p>

<p>I was wondering if a spinning black hole A could complete a Penrose process through another spinning black hole B's ergosphere. i.e. if it could travel through the ergosphere of another spinning black hole and emerge out of it the other side.  What would happen?  Perhaps this is related to the question of whether black holes can orbit each other (in two or three-body system)?  What happens if black holes orbit each other, but their ergospheres overlap?</p>

<black-hole>
Can a black hole undergo a Penrose process inside another black hole's ergosphere?
Sean Roberts
# Can a black hole undergo a Penrose process inside another black hole's ergosphere?

(Asked by: username_0 on 2018-04-27)

I recently watched this video on black holes:
<https://www.youtube.com/watch?v=ulCdoCfw-bY>

And that statement should give you an idea of my level of understanding :)

I was wondering if a spinning black hole A could complete a Penrose process through another spinning black hole B's ergosphere. i.e. if it could travel through the ergosphere of another spinning black hole and emerge out of it the other side. What would happen? Perhaps this is related to the question of whether black holes can orbit each other (in two or three-body system)? What happens if black holes orbit each other, but their ergospheres overlap?

**Tags:** black-hole


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## 2 answers

### Answer by username_2 on 2018-04-27. Score: 5 | Accepted answer

Black holes can orbit each other (we know this from the gravitational waves from their eventual mergers) and there is no particular reason against a small black hole passing through the ergosphere of a large black hole.

The main problem is avoiding a merger. The the two-black hole spacetime has no analytic solution and numeric simulations are messy, but a merger will definitely happen if the event horizons overlap. In any case, a rotating black hole has an ergosphere with an equatorial radius of $2GM/c^2$ and event horizon somewhere between this and the limiting radius $GM/c^2$. If we use the extremal case, then we can presumably just barely fit in nearly an identical mass and rotation black hole in the ergosphere. More likely a much smaller black hole could fit in. The direction of rotation *would* matter for the dynamics, since counter-rotating black holes would tend to coalesce (see [this page](https://duetosymmetry.com/tool/kerr-calculator-v2/) for a plot of the relevant radii and where the [innermost stable circular orbits](https://en.wikipedia.org/wiki/Innermost_stable_circular_orbit) are).

A single black hole passing through the ergoregion would not be able to perform the Penrose process, but we can imagine a binary black hole pair that is ripped apart by tidal forces and then presumably the remaining hole would be ejected with a lot of energy. So, yes, we could get fast small black holes this way.

In practice this system would lose a lot of energy through gravitational waves, making it likely that the holes would coalesce anyway. The exact limits require numerical relativity simulations to estimate, and this one would be a tough one.

(Note that the gravitational waves also carry away energy, up to 1/8 of the total mass of two equal-sized holes merging, but this energy is very hard to capture. Penrose did note in his classic paper that Misner was first in proposing black hole mining using a variant of this.)


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### Answer by username_1 on 2019-01-16. Score: 1

First off blackholes can orbit eachother, we can and have proven that because of the amence energy in the form of gravitational waves they give off which we can measure here on earth.

It's possible that the ergosphere would prolong the mergetion of the two blackholes if they have the correct spin corresponding to the (very unlikely) orbit of the other black hole, although it would almost inevitable fall into one of the event horizons eventually because of the gravitational waves it produces. Which gives off a masive amount of kenetic energy. For the blackhole to gain kenetic energy it would have to overcome this energy loss.


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