Boundary Conditions for $\mathrm{AdS_2}$ Dilaton Gravity

TL;DR

This paper explores a family of AdS2 dilaton gravity models, including JT and Liouville gravity, proposing boundary conditions and verifying their consistency through black hole entropy calculations.

Contribution

It introduces new boundary conditions for a broad class of AdS2 dilaton gravity models and confirms their consistency via entropy analysis.

Findings

Boundary conditions for AdS2 dilaton gravity models are established.

The models include JT and Liouville gravity as special cases.

Black hole entropy calculations confirm the consistency of the boundary conditions.

Abstract

We study a bi-parametric family of dilaton gravity models with constant and negative curvature. This family includes the Jackiw-Teitelboim gravity and the Liouville gravity model induced by a bosonic string. Furthermore, this family is conformally equivalent to the hiperbolic dilaton models. We propose boundary conditions in the Fefferman-Graham and in the Eddington-Finkelstein gauge. We check the consistency of the asymptotic conditions by computing the entropy of their black hole solution.