# Comments on 2D dilaton gravity system with a hyperbolic dilaton potential

## TL;DR

This paper explores a (1+1)-dimensional dilaton gravity model with a hyperbolic potential, revealing new solutions, black hole formation, and thermodynamics insights through Liouville equations and Schwarzian derivatives.

## Contribution

It introduces a novel formulation with new variables leading to Liouville equations and analyzes black hole solutions and thermodynamics in this framework.

## Key findings

- Vacuum solutions exhibit a dipole-like structure.
- A time-dependent solution describes black hole formation from a pulse.
- Black hole entropy matches boundary stress tensor calculations.

## Abstract

We proceed to study a (1+1)-dimensional dilaton gravity system with a hyperbolic dilaton potential. Introducing a couple of new variables leads to two copies of Liouville equations with two constraint conditions. In particular, in conformal gauge, the constraints can be expressed with Schwarzian derivatives. We revisit the vacuum solutions in light of the new variables and reveal its dipole-like structure. Then we present a time-dependent solution which describes formation of a black hole with a pulse. Finally, the black hole thermodynamics is considered by taking account of conformal matters from two points of view: 1) the Bekenstein-Hawking entropy and 2) the boundary stress tensor. The former result agrees with the latter one with a certain counter-term.