# Do White Holes Violate 2nd Law of Thermodynamics?

I have heard (read) much debate over the fundamental problems with white holes, mainly that they violate Thermodynamics by increasing entropy. However, I have also read that a black hole bends space-time enough to "connect" somewhere else as an Einstein-Rosen Bridge. So if the exact same event occurs on both sides of the bridge (time simply reversed), then why does entropy change whatsoever?

PeterDonis
Mentor
I have heard (read) much debate over the fundamental problems with white holes, mainly that they violate Thermodynamics by increasing entropy.

I think you mean "decreasing", correct? I don't know that it's that simple. The usual meaning of "white hole" refers to part of the maximally extended Schwarzschild geometry, which is an idealized mathematical solution to the Einstein Field Equation that nobody believes is physically reasonable. This classical geometry doesn't have any meaningful concept of "entropy" at all, since it is static and can only describe an "eternal" black hole whose mass never changes.

The usual argument for assigning an entropy to a black hole, and for the generalized second law that includes black hole entropy, requires considering processes where things fall into black holes and increase their mass. It also requires considering a physically reasonable way for a black hole to form in the first place, by the gravitational collapse of matter. The spacetime geometries used in these arguments don't contain a white hole region at all. So a "white hole" on this view would have to be the time reverse of the geometries used in these black hole arguments, where we have a hole that things come out of and whose mass decreases--or, ultimately, a hole that spontaneously ejects all its mass and becomes an ordinary star. These processes would indeed violate the second law and are not considered physically reasonable. (To put it another way, there is no way to explain how a white hole in this sense could form in the first place.)

I have also read that a black hole bends space-time enough to "connect" somewhere else as an Einstein-Rosen Bridge. So if the exact same event occurs on both sides of the bridge (time simply reversed)

The Einstein-Rosen bridge does not connect a white hole with a black hole. It connects the "normal" exterior region--the vacuum region outside a black hole/white hole that represents the external universe--with a second exterior region that appears in the maximally extended Schwarzschild geometry and represents a second, separate external universe. Neither exterior region is "before" or "after" the other; the bridge is spacelike and nothing can actually pass through it (it closes up again so fast that even a light ray can't make it through before it closes up and disappears). Nobody really believes the bridge is physically reasonable either.

Thanks, that really clears things up!