Black hole information paradox

The black hole information paradox^[1] is a paradox that appears when the predictions of quantum mechanics and general relativity are combined. The theory of general relativity predicts the existence of black holes that are regions of spacetime from which nothing—not even light—can escape. In the 1970s, Stephen Hawking applied the semiclassical approach of quantum field theory in curved spacetime to such systems and found that an isolated black hole would emit a form of radiation (now called Hawking radiation in his honor). He also argued that the detailed form of the radiation would be independent of the initial state of the black hole,^[2] and depend only on its mass, electric charge and angular momentum.

The information paradox appears when one considers a process in which a black hole is formed through a physical process and then evaporates away entirely through Hawking radiation. Hawking's calculation suggests that the final state of radiation would retain information only about the total mass, electric charge and angular momentum of the initial state. Since many different states can have the same mass, charge and angular momentum, this suggests that many initial physical states could evolve into the same final state. Therefore, information about the details of the initial state would be permanently lost; however, this violates a core precept of both classical and quantum physics: that, in principle only, the state of a system at one point in time should determine its state at any other time.^[3][4] Specifically, in quantum mechanics the state of the system is encoded by its wave function. The evolution of the wave function is determined by a unitary operator, and unitarity implies that the wave function at any instant of time can be used to determine the wave function either in the past or the future. In 1993, Don Page argued that if a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared.^[5] This is called the Page curve.^[6]

It is now generally believed that information is preserved in black-hole evaporation.^[7][8][9] For many researchers, deriving the Page curve is synonymous with solving the black hole information puzzle.^[10]: 291 But views differ as to precisely how Hawking's original semiclassical calculation should be corrected.^{[8][9][11][12]} In recent years, several extensions of the original paradox have been explored. Taken together, these puzzles about black hole evaporation have implications for how gravity and quantum mechanics must be combined. The information paradox remains an active field of research in quantum gravity.