# AdS black holes in two-dimensional dilaton gravity and holography

## TL;DR

This paper introduces two new analytic AdS black hole solutions in two-dimensional dilaton gravity with scalar fields, analyzing their causal structure, thermodynamics, and holographic duals, including extremal cases and boundary theories.

## Contribution

The paper presents two novel analytic AdS black hole solutions with arbitrary parameters, explores their causal structure, thermodynamics, and holographic boundary theories, extending previous models in 2D dilaton gravity.

## Key findings

- Solutions include extremal black holes with constant negative scalar curvature.
- Established a consistent thermodynamics framework including the extremal case.
- Derived a holographic boundary theory characterized by a Schwarzian action with a mass term.

## Abstract

In this paper, we present two novel analytic AdS black hole solutions in a two-dimensional dilaton gravity theory with two scalar fields non-minimally coupled to gravity. Our solutions contain two arbitrary integration constants in the blackening factor $f(r)$, allowing for an extremal configuration. Solution I reproduces a previously reported AdS black hole when one of the integration constants in $f(r)$ vanishes. For our black hole configurations, the scalar curvature is constant and negative, corresponding to the $AdS_2$ spacetime. In order to elucidate their black hole nature, we explore the causal structure of these solutions with the aid of suitable Kruskal-like coordinates and Penrose diagrams. By employing the Hamilton-Jacobi method, we construct a boundary counter-term that renders a renormalized action with a vanishing variation. We use this finite action for the partition function in the semi-classical approximation. We establish a consistent Thermodynamics, verified by the first law, for our black hole solutions, including the extremal case. Finally, we perform a holographic analysis of the effective theory at the boundary of the black hole solution I. This theory is characterized by a Schwarzian action supplemented by a black hole mass term determined by the two integration constants in $f(r)$. We also examine the holographic implications of the boundary counter-term.