Information Loss

TL;DR

The paper analyzes the black hole information loss paradox by reviewing how Hawking radiation entangles exterior modes with interior degrees, leading to a mixed final state for outside observers. It surveys alternatives to information loss and critically examines objections based on unitarity, energy conservation, and AdS/CFT, arguing that none decisively rules out information loss. The authors contend that information loss is a natural outcome of evaporation with the interior acting as a sink, and that resolving the paradox may require new insights into quantum gravity and holography. The work clarifies the conceptual landscape and highlights where precise formulations of holographic dualities are needed for a definitive resolution.

Abstract

The complete gravitational collapse of a body in general relativity will result in the formation of a black hole. Although the black hole is classically stable, quantum particle creation processes will result in the emission of Hawking radiation to infinity and corresponding mass loss of the black hole, eventually resulting in the complete evaporation of the black hole. Semiclassical arguments strongly suggest that, in the process of black hole formation and evaporation, a pure quantum state will evolve to a mixed state, i.e., there will be "information loss." There has been considerable controversy over this issue for more than 40 years. In this review, we present the arguments in favor of information loss, and analyze some of the counter-arguments and alternative possibilities.

Figures (3)

• Figure 1: A spacetime diagram showing the adjoining regions ${\mathcal{U}}_1$ and ${\mathcal{U}}_2$ described in the text. In any physically reasonable state, the quantum field observables in ${\mathcal{U}}_1$ are highly entangled with the quantum field observables in ${\mathcal{U}}_2$.
• Figure 2: A spacetime diagram of a black hole that evaporates. At time $\Sigma_0$ the observables inside and outside the black hole are entangled, just as in Fig. 1. The observables at time $\Sigma_1$ remain entangled with the observables inside the black hole---even though the black hole has evaporated.
• Figure 3: A hyperboloid in Minkowski spacetime lying to the future of a hyperplane. If we consider the evolution of a massless quantum field that initially is in a pure state on the hyperplane, it will be in a mixed state on the hyperboloid.