Integrable models and degenerate horizons in two-dimensional gravity

TL;DR

This paper studies an integrable two-dimensional gravity model, revealing mirror black hole solutions, degenerate ground states, and connections to AdS2 black holes, with implications for semiclassical behavior and Birkhoff's theorem.

Contribution

It introduces an integrable 2D gravity model with mirror black holes and analyzes its solutions, including degenerate states and their relation to Birkhoff's theorem.

Findings

Existence of mirror black hole solutions with the same temperature.

Degenerate constant dilaton ground states similar to Nariai solutions.

Features of the semiclassical theory resembling AdS2 black hole behavior.

Abstract

We analyse an integrable model of two-dimensional gravity which can be reduced to a pair of Liouville fields in conformal gauge. Its general solution represents a pair of ``mirror'' black holes with the same temperature. The ground state is a degenerate constant dilaton configuration similar to the Nariai solution of the Schwarzschild-de Sitter case. The existence of $\phi=const.$ solutions and their relation with the solution given by the 2D Birkhoff's theorem is then investigated in a more general context. We also point out some interesting features of the semiclassical theory of our model and the similarity with the behaviour of AdS$_2$ black holes.