## Is it possible to escape from a black hole using another black hole?

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Eebster the Great
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### Re: Is it possible to escape from a black hole using another black hole?

SuicideJunkie wrote:So basically, even if you had two black holes magically pinned in place, and tried to zing a photon exactly down the line directly between them, it might go past the center of mass, but it couldn't make it out the other side to infinity.

I don't think that's correct. If the black holes are magically pinned in place, then the whole equation changes. (Though exactly how it changes might depend on how the magic works.)

If a photon travels through the event horizon of any black hole, it will end up in the singularity at a finite point in its (proper) future. If it travels through the event horizon of two black holes, it will end up in both singularities. That can only happen if the singularities merge.

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### Re: Is it possible to escape from a black hole using another black hole?

D-503 wrote:If black holes come within their combined Schwarzschild radii of each other are they always destined to merge regardless of their spin and sizes?
No, but if their event horizons touch they are destined to merge.

If they're spinning, their event horizons might be smaller than their Schwarzschild radii.
Eebster the Great wrote:I think the event horizons of Kerr black holes are oblate spheroids, or something similar, and the minor radius is smaller than the Schwarzschild radius.
The event horizon of a Kerr black hole is also a perfect sphere, but of any radius between half and the entire Schwarzschild radius.

The oblate spheroid part is the ergosphere, the place where nothing can stay still, but escape is possible. It's located between the event horizon (touching it at the poles) and the Schwarzschild radius (touching it at the equator).
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gmalivuk
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### Re: Is it possible to escape from a black hole using another black hole?

Here's an article about exactly this question.

There's a video there of a simulated collision between black holes. The horizons do "reach out" to touch ahead of the collision,
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D-503
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### Re: Is it possible to escape from a black hole using another black hole?

gmalivuk wrote:Here's an article about exactly this question.

There's a video there of a simulated collision between black holes. The horizons do "reach out" to touch ahead of the collision,

Great article!
It says that 5 percent of the combined mass is radiated away as gravitational waves which got me wondering about another question. How quickly can a black hole be destroyed? I'm imagining a process where a black hole drives like the ones Isaac Arthur describes in this video
https://youtu.be/oAocMzxPjjo are used to keep two black holes in a stable orbit around eachother that radiates gravitational waves until ones is gone.

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### Re: Is it possible to escape from a black hole using another black hole?

You could use that to get rid of the rotational energy, but not the initial mass.
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### Re: Is it possible to escape from a black hole using another black hole?

There's a relationship between potential energy and rest mass.

As two black holes to from a great distance, to closely orbiting, to merging; potential energy is converted to kinetic energy and kinetic energy is converted to gravitational waves, and the combined black hole has less mass than the sum of the initial black holes.

But there's only so much kinetic energy available at any given distance apart. Adding kinetic energy feeds the black holes more than it allows them to be depleted. (black holes are perfectly inelastic objects, so collisions result in the maximum reduction in kinetic energy possible without violating the laws of momentum).

As black holes get arbitrarily close, arbitrarily large amount of potential energy become "available" as kinetic energy, but time dilation form the combined system becomes important and the outgoing gravitational waves (and outgoing everything else) become red shifted.
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SuicideJunkie
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### Re: Is it possible to escape from a black hole using another black hole?

D-503 wrote:How quickly can a black hole be destroyed?
How small can you make it?
A hole the mass of a large mountain should evaporate completely in about a second IIRC.
Bigger is slower, but some very antique holes could be getting usefully small by now.

Eebster the Great
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### Re: Is it possible to escape from a black hole using another black hole?

The smallest black hole is hypothetically the Planck mass of 22 μg, which has a Schwarzschild radius of twice the Planck length (3.2×10−35 m) and according to formulas developed for large black holes, should evaporate in about 8.7×10−40 s. The properties of micro-black holes are not known, but the assumptions behind this formula certainly break down at such sizes. They may not evaporate at all. For Schwarzschild black holes of a much larger size, you can calculate their various properties using Viktor T. Toth's Hawking Radiation Calculator.

A black hole with a mass of 230 metric tons (smallish 2-story house) has a computed lifetime of 1.0 seconds. A black hole with the mass of a "small mountain" (1012 kg) should have a lifetime of over 2 trillion years.

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### Re: Is it possible to escape from a black hole using another black hole?

And note that, since the CMBR makes the universe uniformly ~2.7K right now, any black hole big enough to radiate at a temperature less than that will be growing, not shrinking. As it turns out, the break-even point is roughly the mass of the moon; anything smaller is hotter than the CMBR and shrinking, while anything larger is colder and growing.

As the universe expands and dilutes the CMBR, lowering the average temperature, gradually those larger holes will become hotter than their surroundings and start shrinking. But it will take a very, very long time.
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Eebster the Great
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### Re: Is it possible to escape from a black hole using another black hole?

It will take a "long time" by ordinary standards, but for black holes with temperatures that are not already far higher than the CMB, their lifetimes are many orders of magnitude longer than it will take for the universe to cool to such a temperature anyway. So from that perspective, there's a negligible blip of time after the formation of the black hole during which it is still growing followed by a vast period of slow evaporation. That blip may be thousands or even millions of times longer than the current age of the universe, but to a black hole, that is hardly even an instant.

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### Re: Is it possible to escape from a black hole using another black hole?

Right. My comment was mostly in response to SJ's line "but some very antique holes could be getting usefully small by now."; old black holes "grew up" in an even hotter universe than now, and generally formed from *much* bigger stars than you can easily find these days, so no, the oldest black holes are generally enormous and still growing.
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Eebster the Great
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### Re: Is it possible to escape from a black hole using another black hole?

Primordial black holes can hypothetically have masses much smaller than a star, and some could have already evaporated.

Pfhorrest
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### Re: Is it possible to escape from a black hole using another black hole?

If the threshold for hot-enough-to-evaporate-in-the-temperature-of-the-current-universe is about the mass of the moon, as someone said upthread, then any otherwise isolated black hole currently just at that mass would have had to have been bigger in the past to have evaporated down to that by now, but the universe would therefore have had to have been colder in the past for it to evaporate down to that, when in fact the universe was hotter in the past. But conversely, a black hole that was too small too far in the past would have already evaporated by now. So any otherwise isolated black hole (not feeding on nearby matter, just background radiation) would have to have started out with some mass smaller than the moon, but large enough to have not evaporated by now. Is there such a mass? How long would it take a moon-sized black hole to evaporate? If that's less than the age of the universe, then no, there is no such mass; anything that started out small enough to have evaporated enough to still be small enough to evaporate today, would have evaporated away entirely by now.

Of course if we consider non-isolated black holes, all kinds of complicated scenarios are possible, where small primordial black holes could have gobbled up nearby matter over their lifetimes while also radiating away energy due to Hawking radiation and have never gobbled up enough matter to get cold enough to stop evaporating, and then only recently run out of matter so that evaporation overtakes its consumption and it's now in the process of evaporating away.
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Eebster the Great
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### Re: Is it possible to escape from a black hole using another black hole?

Pfhorrest wrote:Is there such a mass?

By the Intermediate Value Theorem, yes.

How long would it take a moon-sized black hole to evaporate? If that's less than the age of the universe, then no, there is no such mass; anything that started out small enough to have evaporated enough to still be small enough to evaporate today, would have evaporated away entirely by now.

What?

Black holes with lifetimes on the order of the age of the universe have temperatures in the billions or trillions of kelvins. Black holes with slightly longer lifetimes are still extremely hot. A primordial black hole that formed just after the Big Bang and is evaporating away to nothing right about now should have been four or five orders of magnitude less massive than the Moon when it formed; in the neighborhood of 1011 kg. That's the mass scale.

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### Re: Is it possible to escape from a black hole using another black hole?

Xanthir wrote:And note that, since the CMBR makes the universe uniformly ~2.7K right now
Well, makes the empty parts of the universe "uniformly" 2.7K. Local conditions can be warmer or colder, even naturally.
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### Re: Is it possible to escape from a black hole using another black hole?

Xanthir wrote:And note that, since the CMBR makes the universe uniformly ~2.7K right now
Well, makes the empty parts of the universe "uniformly" 2.7K. Local conditions can be warmer or colder, even naturally.

To a first approximation, all of the universe is empty parts.
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Pfhorrest
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### Re: Is it possible to escape from a black hole using another black hole?

Eebster the Great wrote:
Pfhorrest wrote:Is there such a mass?

By the Intermediate Value Theorem, yes.

The question was whether the lower bound was higher than the upper bound. If it must be less than X and greater than Y but Y is greater than X then there is no solution.

You explained further that X is in fact much lower than Y, which answered my question.
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