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The black hole information paradox is an unsolved problem in physics and a paradox that appears when the predictions of quantum mechanics and general relativity are combined.

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, 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. 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. For many researchers, deriving the Page curve is synonymous with solving the black hole information puzzle.

The calculation of Hawking radiation is performed at the black hole horizon and does not account for the backreaction of spacetime geometry; for a large enough black hole the curvature at the horizon is small and therefore both these theories should be valid. In addition, the argument for information loss relied on the causal structure of the black hole spacetime, which suggests that information in the interior should not affect any observation in the exterior, including observations performed on the radiation the black hole emits. If so, the region of spacetime outside the black hole would lose information about the state of the interior after black-hole evaporation, leading to the loss of information.

In 1993, Page focused on the combined system of a black hole with its Hawking radiation as one entangled system, a bipartite system, evolving over the lifetime of the black hole evaporation. Recent progress in deriving the Page curve for unitary black hole evaporation is a significant step towards finding both a resolution to the information paradox and a more general understanding of unitarity in quantum gravity.

Hawking himself was influenced by this view and in 2004 published a paper that assumed the AdS/CFT correspondence and argued that quantum perturbations of the event horizon could allow information to escape from a black hole, which would resolve the information paradox.

One attempt to resolve the black hole information paradox is known as black hole complementarity. Black hole complementarity suggests that infalling information would be cloned, with one copy falling into the black hole and one copy escaping as Hawking radiation. However, the creators of black hole complementarity argued that, since the infalling copy of the information is only accessible to an infalling observer and the escaping copy of the information is only accessible to an outside observer, it is impossible to observe both copies of the information and therefore the no-cloning theorem is not violated. For a Schwarzschild black hole, it is true that only one copy of the information could be observed, because if the observer waited outside the black hole until the outgoing radiation escaped, they would not be able to reach the infalling radiation before it hit the singularity.

In 2012, the " firewall paradox" was introduced with the goal of demonstrating that black hole complementarity fails to solve the information paradox.

Since the black hole never evaporates, information about its initial state can remain inside the black hole and the paradox disappears.

Quick Facts

• One attempt to resolve the black hole information paradox is known as black hole complementarity.
• 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.
• Since the black hole never evaporates, information about its initial state can remain inside the black hole and the paradox disappears.
• Black hole complementarity suggests that infalling information would be cloned, with one copy falling into the black hole and one copy escaping as Hawking radiation.
• In addition, the argument for information loss relied on the causal structure of the black hole spacetime, which suggests that information in the interior should not affect any observation in the exterior, including observations performed on the radiation the black hole emits.

Source material: Wikipedia - "Black hole information paradox". Adapted and summarized for DiscoverScroll. Original contributors are credited through the linked Wikipedia article. Read original on Wikipedia. CC BY-SA 4.0. Changes were made from the original.