Speed of object emerging from wormhole

[nickyrtr]

Let us say there is a wormhole of the Einstein-Rosen type (maybe physically impossible, I know, but just assume somehow it exists). A 'rain observer' falls from rest at a large distance into the black hole, then emerges from the white hole on the other side.

My question is, what is the speed of the object (relative to the white hole) when it has traveled far away from the white hole? Is the speed zero, or did it pick up a boost of kinetic energy during the trip through the wormhole?

 

[zhermes]

There is no reason why it would pick up kinetic energy. Doing so would most-likely violate energy conservation, and more simple, an ER-bridge is symmetric, so there would be no source of impulse.

 

[nickyrtr]

... an ER-bridge is symmetric, so there would be no source of impulse.

Is the ER-bridge really symmetric? I thought that an outside observer can distinguish a black hole from a white hole.

 

[zhermes]

Is the ER-bridge really symmetric? I thought that an outside observer can distinguish a black hole from a white hole.

We're getting into dangerous territory here. If you look at the simplest mathematical description of a wormhole, BOTH ends LOOK like black-holes--and that's okay because the neck is infinitely narrow preventing anything from moving through (i.e. no contradiction). Honestly I have no idea what the more complex treatments (e.g. where the neck is widened by negative energy density etc) really look like mathematically, but I really don't think you could have any stable asymmetries. My guess is that in those complex cases, neither end looks like a black-hole anymore (i.e. no event horizon).

 

[George Jones]

Let us say there is a wormhole of the Einstein-Rosen type (maybe physically impossible, I know, but just assume somehow it exists). A 'rain observer' falls from rest at a large distance into the black hole, then emerges from the white hole on the other side.

How does this happen? Have you seen a spacetime diagram of this situation?

 

[nickyrtr]

How does this happen? Have you seen a spacetime diagram of this situation?

OK, I see what you are getting at. On a spacetime diagram of a (non-rotating) black-hole, there are no trajectories leading into the black hole and then out of the white hole. This would have to be a rotating (Morris-Thorne?) wormhole for the question to make any sense.

So let me rephrase the question. If an object falls from rest at a large distance into a traversable wormhole, then travels away from the opposite end of the wormhole to a large distance, what will its speed be, relative to the wormhole?

 

[Nabeshin]

To some extent the answer to this question depends on the particular geometry (and topology) of the wormhole in question. For the simplest case of an inter-universal lorentzian wormhole, you will experience no net energy gain (if you started from infinity, you will end at infinity).

It's not that difficult to construct intra-dimensional wormhole geometries which appear to lead to violation of conservation of energy. For an in depth discussion, see Matt Visser's Lorentzian Wormholes.

 

[nickyrtr]

...For the simplest case of an inter-universal lorentzian wormhole, you will experience no net energy gain (if you started from infinity, you will end at infinity)...

Thanks everyone for the replies. Answers here, and suggested readings, gives me a new picture of the 'white hole' .. previously I had thought of it as an anti-black-hole, with a sort of repulsive anti-gravity, but from what I gather now that is the wrong picture. It seems a white hole is actually identical to a black hole, at least in that they both are attractive centers of gravity. The only difference is that matter emerges from the white hole horizon, whereas it is consumed by a black hole horizon. Is that an accurate description?

If so, perhaps either end of the wormhole could be both a white and black hole at the same time, if matter were traveling through it simultaneously in opposite directions.

 

[George Jones]

Actually, there are quite a few differences between a white hole and a black hole. I hope to get back to this thread, but, if I don't, for now I'll say that a black hole conforms to the Hays Code while a white hole doesn't.

 

[nickyrtr]

Actually, there are quite a few differences between a white hole and a black hole. I hope to get back to this thread, but, if I don't, for now I'll say that a black hole conforms to the Hays Code while a white hole doesn't.

Does the space-time near a black hole have a different metric than near a white hole?

 

[George Jones]

Actually, there are quite a few differences between a white hole and a black hole. I hope to get back to this thread, but, if I don't, for now I'll say that a black hole conforms to the Hays Code while a white hole doesn't.

Here, I meant that a black hole singularity is clothed in an event horizon, while a white hole singularity is naked.

Does the space-time near a black hole have a different metric than near a white hole?

The Schwarzschild components of a Schwarzschild black hole metric look the same in black hole regions and white hole regions only because of "symbol overloading". in the white hole region, [itex]r[/itex] is a future-directed timelike coordinate, while in the black hole region, [itex]r[/itex] is a past-directed timelike coordinate. Outside of the black and white hole regions, [itex]r[/itex] is a spacelike coordinate

I hope to get back to this thread with more expansive comments on Schwarzschild black holes, Schwarzschild white holes, and Morris-Thorne wormholes. My comments so far are probably a bit cryptic, but, before I expand on them, it would be good to think about the question:

In general, what, mathematically, is a coordinate chart (coordinate system) in general relativity?

 

[JesseM]

It seems a white hole is actually identical to a black hole, at least in that they both are attractive centers of gravity. The only difference is that matter emerges from the white hole horizon, whereas it is consumed by a black hole horizon. Is that an accurate description?

Another difference is that for an observer who starts out outside the event horizon of a black hole, they can reach the event horizon in finite proper time, but this wouldn't be possible for an observer who starts out outside the event horizon of a white hole (an object falling towards the white hole would either keep falling towards it forever without reaching the horizon, or would fall until the white hole itself 'explodes' in something like the time-reverse of the formation of a black hole from collapsing matter). And any object inside the event horizon of a white hole will have the singularity in its past and will inevitably cross the event horizon in the outward direction in its future, whereas any object inside the event horizon of a black hole will have crossed the event horizon in its past and will inevitably hit the singularity in its future (at least if we're talking about a nonrotating, uncharged black hole and white hole).

 

[nickyrtr]

..an object falling towards the white hole would either keep falling towards it forever without reaching the horizon, or would fall until the white hole itself 'explodes' in something like the time-reverse of the formation of a black hole from collapsing matter...

That sounds a lot like a repulsive force away from the white hole. Is there some range of distance outside the white hole horizon where a hovering observer (constant r, no transverse momentum) experiences acceleration away from the white hole?