Deformations of JT Gravity and Phase Transitions

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.

arXiv comment17 pp, added references in v. 3, added comment on phase transitions at zero temperature

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• Equivalence of JT Gravity and Near-extremal Black Hole Dynamics in Higher Derivative Theory
• Page curve from dynamical branes in JT gravity
• Universal flow equations and chaos bound saturation in 2d dilaton gravity
• Real Classical Geometry with arbitrary deficit parameter(s) $\alpha {(}_I)$ in Deformed Jackiw-Teitelboim Gravity
• Deformations of JT Gravity via Topological Gravity and Applications
• The complex Liouville string: the gravitational path integral
• Pacman geometries and the Hayward term in JT gravity
• Nonsingular black hole in two-dimensional asymptotically flat spacetime
• The quantum $p$-spin glass model: A user manual for holographers
• Two-dimensional (bi-)scalar gravities from four-dimensional Horndeski