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

TL;DR

The work studies a two-dimensional dilaton gravity system with a hyperbolic dilaton potential, framed as a deformation of JT gravity. It introduces two auxiliary variables to recast the theory into two Liouville sectors with Schwarzian-type constraints, enabling a tractable analysis of vacuum geometries and time dependent black hole formation. The analysis extends to include conformal matter, deriving a deformed black hole and demonstrating that the Bekenstein-Hawking entropy agrees with a boundary-stress-tensor computation after an appropriate counter-term. The results reveal a dipole-like vacuum structure, a concrete deformed black hole solution, and suggest connections to holography and deformed Schwarzian theories.

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.