Mass distribution behavior of the singularities during black hole mergers

[DarkMattrHole]

Thanks all. I've looked at a number of trousers diagrams now and will dig deeper. The impression I'm getting from this discussion is that there is essentially nothing inside the horizon at all to an outside observer, not even space, space is not part of the inside of a BH, the horizon is a barrier (from outside view) - like an edge in space, but an edge that recedes as you approach it, and any time that is ticking and marking off change, must be taking place in material at or outside the horizon where spacer exists for things to happen or stop happening. How close is that? Also that lower dimensional drawings of BHs, with central singularity indicated are depicting an end to all futures, not a place, and there's no good way to draw a diagram of two BHs merging the way we can draw various diagrams of a single black hole. Things sure get interesting when all four dimensions including time get into play.

I found an interesting trousers model (trousers with pantaloons) here..
..."suggests a possibility of proving the Penrose inequality mathematically for generic astrophysical binary back hole configurations."
https://www.aei.mpg.de/2420822/what-happens-inside-a-black-hole-merger

 

[PeterDonis]

The impression I'm getting from this discussion is that there is essentially nothing inside the horizon at all to an outside observer, not even space

The fact that the outside observer cannot see inside the horizon does not mean the outside observer thinks there is nothing there.

space is not part of the inside of a BH

This is not correct. Spacetime is still 4-dimensional inside the horizon, and at every event one can still find an orthonormal tetrad of one timelike vector and three spacelike vectors, so one can still split spacetime into "space" and "time" locally. The global behavior is what is highly counterintuitive.

the horizon is a barrier (from outside view)

No, it isn't. It's perfectly possible to fall inside the horizon. You just can't get back out again once you're inside.

like an edge in space, but an edge that recedes as you approach it

I don't know where you are getting all this from, but it's wrong.

any time that is ticking and marking off change, must be taking place in material at or outside the horizon where spacer exists for things to happen or stop happening

This is wrong. Time ticks perfectly normally for an observer falling through the horizon and on inside the hole.

lower dimensional drawings of BHs, with central singularity indicated are depicting an end to all futures, not a place

Yes.

there's no good way to draw a diagram of two BHs merging the way we can draw various diagrams of a single black hole

Yes. To put it another way, even the minimum amount of distortion you can have in a diagram of a BH merger is far more distortion than you need to have in a diagram of a single BH.

 

[PeterDonis]

I found an interesting trousers model (trousers with pantaloons) here

Note that what this paper is calling a "horizon" is not precisely the same as what we have been calling a "horizon" in this thread. We have been using the term "horizon" to mean the event horizon--the boundary of the region in spacetime that cannot send light signals to infinity. When I say there is only one horizon, shaped (heuristically) like a pair of trousers, it is the event horizon I mean.

This paper is using the term "horizon" to mean "Marginally Outer Trapped Surface" (or MOTS), which is also referred to as an "apparent horizon". Heuristically, it is a surface at which a spherical radially outgoing wave front of light does not increase in area. In a stationary black hole (i.e., an idealized black hole that isn't merging with another one, and isn't absorbing any matter, and isn't evaporating), the apparent horizon coincides with the event horizon; but in any dynamic situation, like a merger, or a black hole with matter falling into it, or an evaporating black hole (when we take quantum effects into account), the two kinds of horizon no longer coincide. In the case of a merger, the event horizon will in general be outside of any apparent horizons.

The other key difference with apparent horizons is that there can be more than one of them, and they can even overlap and self-intersect, as the paper describes. So you can't really view them as a single "boundary" of a black hole, the way you can view the event horizon. But they are useful in trying to picture what goes on inside the horizon as the merger proceeds and the final hole settles down.