Eventide ProphetPhenomenon: Information Loss at the Event Horizon

Eventide Prophet stands at the horizon holding a question nobody has answered: when a black hole evaporates, where does what fell in go?

Start with what is established on paper. In 1972 Jacob Bekenstein argued that black holes carry entropy. In 1974 Stephen Hawking found that they radiate, with the temperature in the first formula, and that fixed the entropy, the second formula, proportional to the horizon's area. A black hole left alone shrinks as it radiates, and in principle can vanish entirely.

The trouble is what the radiation looks like. In Hawking's calculation it is exactly thermal: its details depend on the black hole's mass, charge and spin and nothing else. Throw in an encyclopaedia or an equal mass of sand and the glow coming out is the same. If the black hole disappears and only that glow is left, the information about the encyclopaedia is gone. In 1976 Hawking argued just that. Quantum mechanics, as normally understood, forbids it: the exact state now determines the exact state before.

In 1993 Don Page sharpened the problem. If information does get out, the entanglement entropy of the radiation, the third line on this page, must rise at first and then fall back to zero, and it can never exceed the black hole's own entropy. Hawking's original calculation never turns over. Recent theoretical work has found ways to reproduce Page's turnover, and many physicists now expect information is preserved. How it gets out, through what physics, and whether those calculations capture real black holes, are not settled. Hawking radiation itself has never been observed.

This is the black hole information paradox. It is open.

Eventide Prophet waits at the edge. The question has not been answered, only asked better.