Quantum Black Holes and Gauge/Gravity Duality

Abstract: From a conceptual point of view, this chapter may be viewed as an exercise in combining quantum field theory and general relativity in a controlled setting. Despite its apparent simplicity, this exercise is deeply rooted in highly non-trivial developments in superstring theory and holography, and it addresses what is arguably one of the most profound questions in quantum gravity: the fate of information in black hole evaporation. For this reason, one is naturally compelled to examine this exercise as carefully as possible, closely following the original authors. This chapter presents thus a detailed overview of recent work by Almheiri et al. and Penington on the AdS2 black hole information loss paradox and its proposed resolution within the framework of the AdS/CFT correspondence. The roles of generalized entanglement entropy, quantum extremal surfaces, the island conjecture, holography, and replica wormholes in this resolution are discussed in detail. The distinction between the von Neumann entropy and the Bekenstein-Hawking entropy in black hole physics is carefully clarified. It is shown that a phase transition at the Page time, between the trivial quantum extremal surface at the horizon and a non-vanishing quantum extremal surface located behind the horizon, leads to the correct Page curve. A simplified version of the information loss problem for the eternal AdS2 black hole, together with its resolution along similar lines, is also presented. The replica trick and its crucial role in computing entanglement entropies for various intervals in AdS2 are discussed at some length. However, the use of the replica trick in constructing replica wormholes that dominate the Euclidean path integral, thereby leading to the island rule and the correct quantum extremal surfaces, is only outlined.