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An observer A can cross the event horizon of a black hole in a finte proper time, while a far-away observer B would say it takes an infinite time for observer A to reach the event horizon.

Now consider a black hole merger, I am imagining a very small black hole falling into a larger one. These answers describe and explain some details about the merging as seen from a far-away observer: 1 2 3.

Now to my questions: Just as I can describe an infalling observer from its point of view in a well defined way, is there a way to describe an infalling black hole from its point of view in a well defined way? If yes, does it cross the horizon in a finite proper time?

There is a chance that my question is nonsensical and ill defined.

Something better defined would be to consider an observer comoving with the small black hole that is falling inside the large event horizon at the same time as the small black hole. This observer and the small black hole are kind of moving on parallel trajectories as they enter the very large event horizon. In particular I'd like to know how the observer describe what's happening just before the merging, and after the observer enters the event horizon, does it keep seeing the small black hole moving as it was before?

RenatoRenatoRenato
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1 Answers1

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A black hole cannot really be considered as an observer. Observers have timelike world lines while black holes have horizons that are lightlike surfaces and they have spacelike singularities.

I am unaware of any calculations from the perspective of such a co-falling observer. However, this process is pretty well understood because it is important for gravitational wave astronomy. So, it is possible to describe it in terms of invariant things that are independent of any observer.

As the small black hole approaches, the spacetime is not spherically symmetric and is no longer well described by the Schwarzschild metric. The event horizon of the big black hole bulges upwards to meet the horizon of the small black hole. The resulting spacetime, with a single non-spherical event horizon, radiates gravitational waves and the event horizon becomes more spherical. This process is pretty fast.

There is no analytical description of this spacetime. But as I mentioned above, it is well understood through numerical calculations.

Dale
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