Deformations of JT Gravity and Phase Transitions

Understand

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.