Can we distinguish between black holes and white holes?

[Khashishi]

I know white holes probably don't exist, but I'm having trouble understanding how someone outside the white hole would perceive them. My understanding is that they are time-reversed black holes. I've read that nothing can fall into a white hole, that it is repulsive, and that it continually ejects things out.

But... when I try to reason out what a time-reversed black hole would actually look like, I get a black hole. I mean, I get something which seems to behave the same as a black hole, at least from an observer outside the hole.

It's possible to orbit a black hole. After all, the gravity outside a spherical planet is supposed to be the same as the gravity at the same distance from a black hole of the same mass. If you play a video of a stable orbit in reverse, you get a stable orbit. So it should be possible to orbit a white hole. So a white hole is not repulsive, but attractive, just like a black hole. Would we, in fact, be able to tell them apart?

I looked at the diagram in:
http://en.wikipedia.org/wiki/Kruskal–Szekeres_coordinates
where black hole and white hole seem clearly different. But, can we actually identify the top and bottom singularities (topologically tie them together, so coordinate T loops around endlessly). Then a black hole and a white hole are the same thing.

 

[PeterDonis]

My understanding is that they are time-reversed black holes.

Sort of. See below.

I've read that nothing can fall into a white hole, that it is repulsive, and that it continually ejects things out.

The first is true; the second is not; the third is sort of true (it depends on what exactly you mean by "white hole"--see below).

The reason nothing can fall into a white hole is that its horizon is an ingoing null surface--in other words, the horizon is moving inward at the speed of light. So no matter how fast you move inward, the horizon is moving inward faster than you are, so you can never catch it. (Notice that if you replace "inward" with "outward", you get a description of why you can't escape a black hole.) However, that does not mean you are safe if you fall towards a white hole; see below.

A white hole's gravity is not repulsive; it is attractive, just like a black hole's. If we have a family of observers who are "hovering" at fixed altitudes above the hole, they will see freely falling objects appear to accelerate downward due to the hole's gravity. However, the real question is, where do those objects end up? The answer is, they end up inside the black hole, not the white hole.

In other words, if you fall "towards" a white hole, you won't end up inside the white hole, but you will end up inside a black hole--the black hole that is "connected" to the white hole. That is, if we are looking at the Kruskal diagram of the maximally extended Schwarzschild spacetime, and we are in region I, the exterior region on the right of the diagram, we can move radially inward, and it may seem like we are falling towards the white hole when we do (if, for example, we are in the lower part of region I, near the white hole horizon), but we can never end up in the white hole region (the interior region at the bottom); we will always end up in the black hole region (the interior region at the top).

All of the above was talking about an idealized white hole/black hole spacetime which is vacuum everywhere--in this spacetime, the white hole doesn't eject anything except idealized "test objects" that don't affect the spacetime geometry. But we could consider a different spacetime, with a white hole that ejects significant mass--for example, one that "explodes" a large quantity of matter out of it, like the time reverse of a star collapsing to form a black hole. In this spacetime, if we assume that the matter is ejected fast enough that it does not recollapse to a black hole, the white hole singularity ends up disappearing, and so does the white hole horizon; in their place, there is just an expanding cloud of matter of gradually decreasing density. (Note that this is not the same as an expanding FRW universe model such as the ones used in cosmology; those spacetimes do not have a white hole horizon or a past null infinity outside it.) If you fall towards the white hole, you will just end up inside the expanding cloud of matter, and you won't find any singularity or horizon in there; you'll just either stay inside it or end up coming back out.

can we actually identify the top and bottom singularities (topologically tie them together, so coordinate T loops around endlessly).

No. At least, not if you want to satisfy the Einstein Field Equation.

 

[Khashishi]

Thanks. There seem to be a lot of misleading popularizations of the subject.
I suppose we need quantum gravity to tell us what happens at the singularity.

 

[rootone]

Remember,that singularity isn't a physical object, it's a condition of spacetime that our best theories cannot describe.
If we do succeed with a sensible quantum gravity theory, the singularity will probably disappear.