What is the black hole information paradox?

The black hole information paradox is an unsolved problem that appears when general relativity and quantum mechanics are combined. In the 1970s Stephen Hawking showed that a black hole emits radiation and can evaporate completely. His calculation suggested that the radiation carries no record of what fell in, which would mean that information is permanently lost. That conflicts with a core rule of quantum physics called unitarity. [1] [2]

Hawking realized that at an event horizon, which can be crossed only inward, two virtual particles can become separated. One falls in and the other radiates away with some energy, so the black hole shrinks. Hawking found that this radiation depends only on the black hole's mass, electric charge and angular momentum. Many different initial states share those values, so many starting situations would end in the same final radiation. A black hole formed from a library and one formed from a featureless rock would look alike. [2] [1] [3]

In quantum mechanics, a system's wave function evolves through a unitary operator, so the wave function at one moment can in principle determine the past and the future. Information destroyed by a black hole would break that rule. A physicist writing in MIT's departmental magazine argues that this would be an unprecedented loss of determinism, since no other known process causes net information loss. [1] [4]

A notepad thrown into a fire seems to lose its message, but with perfect knowledge of every molecule and the exact equations governing them, one could in principle reconstruct the message from the ash. Evaporating black holes appear different. The MIT account says the radiation must be thermal and indistinguishable between any two evaporated black holes, so even complete knowledge of the final state would not reveal what went in. [4]

The same account notes that gravity at the horizon of a large black hole such as M87 is weaker than at the Sun's surface, so ordinary semiclassical gravity should work there. That leaves two unappealing options: strong quantum gravity effects in places that look ordinary, or a non-deterministic physics. [4]

In 1993 Don Page argued that if evaporation is unitary, the entropy of the radiation should rise and then fall back to zero, a shape now called the Page curve. Hawking's calculation instead gives an entropy that rises until evaporation ends. It is now generally believed that information is preserved, and for many researchers, deriving the Page curve is equivalent to solving the puzzle. [1]

In 2019, two sets of researchers, one including Engelhardt and colleagues and another by Penington, reported a different semiclassical analysis consistent with the Page curve. Even so, views differ on exactly how Hawking's original calculation should be corrected, and the problem remains an active area of quantum gravity research. The search results do not describe the competing proposals in detail. [4] [1]