Einstein on Black Holes and White Holes

While Einstein and Planck had lunch today at a small restaurant near the Leman Lake, one of the French Gifts of the Alpes, the discussion on White Holes and Black Holes had continued.

Black hole horizons can only absorb matter, while white hole horizons ostensibly recede from any incoming matter at the local speed of light, so that the infalling matter never crosses. The infalling matter is then scattered and reemitted at the death of the white hole, receding to infinity after having come very very close to the final singular point where the white hole is destroyed. The total proper time until an infalling object encounters the singular endpoint is the same as the proper time to be swallowed by a black hole, so the white hole picture does not say what happens to the infalling matter. Ignoring the classically unpredictable emissions of the white hole, the white hole and black hole are indistinguishable for external observers.

In quantum mechanics, the black hole emits Hawking radiation, and so can come to thermal equilibrium with a gas of radiation. Since a thermal equilbrium state is time reversal invariant, Hawking argued that the time reverse of a black hole in thermal equilibrium is again a black hole in thermal equilibrium.^[1] This implies that black holes and white holes are the same object. The Hawking radiation from an ordinary black hole is then identified with the white hole emission. Hawking's semi-classical argument is reproduced in a quantum mechanical AdS/CFT treatment^[2], where a black hole in Anti De Sitter space is described by a thermal gas in a gauge theory, whose time reversal is the same as itself.

White holes appear as part of the vacuum solution to the Einstein field equations describing a Schwarzschild wormhole. One end of this type of wormhole is a black hole, drawing in matter, and the other is a white hole, emitting matter. While this gives the impression that black holes in this universe may connect to white holes elsewhere, this turns out not to be the case for two reasons. First, Schwarzschild wormholes are unstable, disconnecting as soon as they form. Second, Schwarzschild wormholes are only a solution to the Einstein field equations in vacuum (when no matter interacts with the hole). Real black holes are formed by the collapse of stars. When the infalling stellar matter is added to a diagram of a black hole's history, it removes the part of the diagram corresponding to the white hole [1].

The existence of white holes that are not part of a wormhole is doubtful, as they appear to violate the second law of thermodynamics.

Quasars and active galactic nuclei are observed to spew out jets of matter. This is now believed to be the result of polar jets formed when matter falls into supermassive black holes at the centers of these objects. Prior to this model, white holes emitting matter were one possible explanation proposed.

A more recently proposed view of black holes might be interpreted as shedding some light on the nature of classical white holes. Some researchers proposed that when a black hole forms, a big bang occurs at the core which creates a new universe that expands into extra dimensions outside of the parent universe^[3].

The initial feeding of matter from the parent universe's black hole and the expansion that follows in the new universe might be thought of as a cosmological type of white hole. Unlike traditional white holes, this type of white hole would not be localized in space in the new universe and its horizon would have to be identified with the cosmological horizon.