Two-dimensional Quantum Black Holes, Branes in BTZ and Holography

TL;DR

This paper constructs and analyzes a quantum black hole solution in two dimensions, demonstrating its thermodynamic stability, holographic correspondence with a boundary CFT, and temperature equivalence with a BTZ black hole.

Contribution

It provides a novel semiclassical 2D black hole solution, links it holographically to a boundary CFT, and shows temperature matching with the BTZ black hole.

Findings

Quantum black hole is thermodynamically stable.

Geometry matches between 2D solution and BTZ black hole.

Black hole temperature equals the bulk BTZ temperature.

Abstract

We solve semiclassical Einstein equations in two dimensions with a massive source and we find a static, thermodynamically stable, quantum black hole solution in the Hartle-Hawking vacuum state. We then study the black hole geometry generated by a boundary mass sitting on a non-zero tension 1-brane embedded in a three-dimensional BTZ black hole. We show that the two geometries coincide and we extract, using holographic relations, information about the CFT living on the 1-brane. Finally, we show that the quantum black hole has the same temperature of the bulk BTZ, as expected from the holographic principle.