Information paradox

The paradox originates from the combination of black hole thermodynamics and quantum field theory in curved spacetime. In 1974, Stephen Hawking showed that quantum effects near the event horizon cause a black hole to emit thermal radiation, now called Hawking radiation¹. This radiation carries no information about the interior state, implying that a black hole that forms from a pure quantum state evaporates into a mixed state—a loss of information. Jacob Bekenstein had earlier argued that black holes have entropy proportional to their horizon area, the Bekenstein-Hawking entropy². The problem is that if the final radiation is purely thermal, the initial pure state evolves into a mixed state, violating quantum unitarity. This tension between general relativity and quantum mechanics is the information paradox.

Several resolutions have been proposed. The holographic principle, later formalized as the AdS/CFT correspondence by Juan Maldacena in 1997, suggests that a theory of quantum gravity in a space can be fully described by a lower-dimensional quantum field theory on its boundary, implying that information is not lost³. Black hole complementarity posits that no observer sees a violation of unitarity: an infalling observer experiences normal physics, while an outside observer sees information encoded in the radiation. The firewall paradox (AMPS 2013) challenged this by showing that complementarity may conflict with quantum entanglement and the equivalence principle⁴. More recently, calculations using the Page curve—a measure of entanglement entropy—have shown that information can be recovered from the radiation after the black hole has emitted more than half its mass, preserving unitarity⁵.

Beyond the mainstream, several niche ideas have emerged. The ER=EPR conjecture (Maldacena and Susskind, 2013) proposes that wormholes (Einstein-Rosen bridges) are equivalent to quantum entanglement (EPR pairs), offering a geometric mechanism for information transfer⁶. The Hayden-Preskill thought experiment (2007) showed that if a black hole is a fast scrambler, an observer can recover information from a black hole after a short time, provided they have a copy of the interior state. Another subtlety is the stretched horizon—a membrane just outside the event horizon—used in the black hole complementarity picture to store information temporarily. The firewall paradox also led to debates about the equivalence principle: some argue that firewalls contradict the principle that free-falling observers see nothing special at the horizon, while others claim that the paradox forces a revision of our understanding of spacetime.

As of 2025, the information paradox is widely considered resolved in the context of the AdS/CFT correspondence, where unitarity is guaranteed by construction. However, the mechanism for information retrieval in asymptotically flat spacetime remains debated. The Page curve calculations, extended to flat space by Penington, Almheiri, and others, show a consistent picture: the entanglement entropy of the Hawking radiation follows a curve that rises then falls, matching the Page curve expected for a unitary process⁵. These results rely on the quantum extremal surface prescription and island formula, which suggest that late-time radiation includes contributions from regions behind the horizon. Open questions include whether the interior of an evaporating black hole is described by a smooth spacetime or by a firewall, and whether the resolution extends to cosmological horizons. The paradox remains a testing ground for any theory of quantum gravity.

Hawking radiation

Thermal radiation emitted by black holes due to quantum effects near the event horizon, predicted by Stephen Hawking in 1974.

Bekenstein-Hawking entropy

The entropy of a black hole, proportional to the area of its event horizon, given by S = kA/4ℓP².

AdS/CFT correspondence

A duality between a theory of gravity in anti-de Sitter space and a conformal field theory on its boundary, providing a non-perturbative formulation of quantum gravity.

Firewall paradox

A paradox proposing that an observer falling into a black hole encounters a high-energy firewall at the horizon, violating the equivalence principle.

Page curve

The expected behavior of entanglement entropy of Hawking radiation if information is preserved, initially rising and then falling after the Page time.

ER=EPR

The conjecture that Einstein-Rosen bridges (wormholes) are equivalent to Einstein-Podolsky-Rosen quantum entanglement pairs.

Black hole complementarity

The principle that no single observer can witness both the interior and exterior descriptions of a black hole, avoiding paradoxes.