Deformations of JT Gravity and Phase Transitions

TL;DR

This paper investigates phase transitions and deformations in two-dimensional dilaton gravity, revealing conditions for black hole solutions with different thermodynamic properties and identifying possible first order phase transitions akin to Hawking-Page transitions.

Contribution

It demonstrates that in deformed JT gravity, black hole solutions exhibit phase transitions and thermodynamic behaviors, extending understanding of 2D gravity models.

Findings

Existence of black hole solutions with negative and positive specific heat at the same temperature.

Monotonic increase of energy and entropy with temperature, with possible discontinuities.

Presence of first order phase transitions similar to Hawking-Page transition.

Abstract

We re-examine the black hole solutions in classical theories of dilaton gravity in two dimensions. We consider an arbitrary dilaton potential such that there are black hole solutions asymptotic at infinity to the nearly $\mathrm{AdS}_2$ solutions of JT gravity, and such that the black hole energy and entropy are bounded below. We show that if there is a black hole solution with negative specific heat at some temperature $T$, then at the same temperature there is a black hole solution with lower free energy and positive specific heat. As the temperature is increased from 0 to infinity, the black hole energy and entropy increase monotonically but not necessarily continuously; there can be first order phase transitions, similar to the Hawking-Page transition. These theories can also have solutions corresponding to closed universes.