Information Loss in Black Holes

TL;DR

The work argues that information is not lost in black hole formation and evaporation when quantum gravity is treated via Euclidean path integrals that sum over spacetime topologies. By comparing topologically trivial saddles, which yield unitary evolution with $Z(\beta)=\mathrm{Tr}(e^{-\beta H})$, to non-trivial black-hole saddles that cause correlators to decay, it shows that information preservation arises from the trivial sector while apparent loss appears in the black-hole sector but is resolved in the full topological sum. The analysis leverages AdS/CFT insights to reconcile unitarity with dissipative behavior in the black-hole channel, and extends to small black holes via thermal fluctuations, where action differences govern observability of such states. Overall, the paper contends that information is preserved in quantum gravity, with Hawking radiation understood as tunneling from inside the horizon rather than true information destruction, and emphasizes the crucial role of topology in ensuring unitarity. $Z(\beta)=\int DgD\phi e^{-I[g,\phi]}=\mathrm{Tr}(e^{-\beta H})$ and other topological distinctions underpin the argument, particularly within asymptotically AdS settings where the path integral is well-defined.

Abstract

The question of whether information is lost in black holes is investigated using Euclidean path integrals. The formation and evaporation of black holes is regarded as a scattering problem with all measurements being made at infinity. This seems to be well formulated only in asymptotically AdS spacetimes. The path integral over metrics with trivial topology is unitary and information preserving. On the other hand, the path integral over metrics with non-trivial topologies leads to correlation functions that decay to zero. Thus at late times only the unitary information preserving path integrals over trivial topologies will contribute. Elementary quantum gravity interactions do not lose information or quantum coherence.