The causal structure of black holes

[sharp_blue]

A commenter writing about my earlier post, "Relativity, FTL and Causality" said:

As far as FTL being equivalent to time travel, the above explanation is correct. As far as FTL being impossible at present, it is not quite. Richard's explanation lacks a mention of black holes. An object (with non-zero mass), falling into a black hole from rest, will

Comments

[sharp_blue]

Black holes that result from the collapse of stars aren't time symmetrical, which is why I chose to discuss them rather than the full Schwarzschild solution, which is the spacetime of a static, eternally existing, uncharged spherically symmetric black hole. The full Schwarzschild solution has a more complex causal structure with both past and future singularities and two asymptotically flat exterior vacuum regions, and is symmetric under time reversal. The spacetime outside any uncharged, non-rotating spherical body is just like a patch of the Schwarzschild solution and this is typically joined to a different metric within the body. (As the body collapses the non-Schwarzschild region shrinks away to nothing.)

A time-inverted astrophysical black hole would be a "white hole". There would be particles that originated on the past singularity and streamed out through the event horizon. Any particles that emerged from the horizon would not be able to re-enter the white hole. The white hole would shrink away to nothing as it lost mass. (This is a different process to the shrinking of a black hole under Hawking radiation.)

When quasars were first discovered some people thought they might be powered by white holes but this theory fell out of favour as accretion onto black holes became better understood. There's currently no evidence of white holes existing at all. A natural question is then: why do we see black holes but not white holes? The best answer we have at the moment is that it's a matter of thermodynamics. The event horizons of black holes are now known to have an associated entropy (which is proportional to the area of the horizon for most (all?) classes of black hole). It's been estimated that a black hole formed from the collapse of a star might have an entropy 10^19 times as high as the original star. A white hole spewing out matter would thus be decreasing entropy at a ferocious rate, which is not the sort of thing we observe because it violates the second law of thermodynamics.

(The idea of black holes having a temperature and entropy first arose from the study of quantum fields in the curved classical spacetime outside the horizon, and the prediction of Hawking radiation. It was a really rather mysterious thing as the classical black hole has no microstates to give it an entropy. However, it's now possible to use loop quantum gravity and perhaps superstring theory to calculate the entropy of the event horizon directly by counting microstates of the quantum geometry, so perhaps it's a little less mysterious than it once was.)

[ashley_y]

As I understand it, a black hole cannot be destroyed, except by evaporation through Hawking radiation. Would that mean that a white hole cannot be created except by somehow time-reversing Hawking radiation?

Secondly, I assume a black hole can exist without gaining mass if there's nothing around to absorb. So presumably a white hole can exist and not spew anything out, and thus not decrease entropy? This seems to be the most likely behaviour of a white hole were one to exist in this universe of increasing entropy.