Nonsingular black hole in two-dimensional asymptotically flat spacetime

TL;DR

This paper presents an exact solution for a nonsingular, asymptotically flat two-dimensional black hole that features a gravitational domain wall, with thermodynamic properties analyzed and positive entropy and energy for certain parameter ranges.

Contribution

It introduces a novel two-dimensional dilaton gravity model with an exact nonsingular black hole solution and analyzes its global structure and thermodynamics.

Findings

The solution describes a nonsingular black hole with a gravitational domain wall.

Thermodynamic quantities are positive for specific parameter ranges.

The spacetime exhibits a kink profile with a horizon but no singularity.

Abstract

We study a special two-dimensional dilaton gravity with Lagrangian $\mathcal{L}=\frac{1}{2}\sqrt{-g}(\phi R+{\lambda^2}{\rm sech}^2\phi)$ where $\lambda$ is a parameter of dimension mass. This theory describes two-dimensional spacetimes that are asymptotically flat. Very interestingly, it has an exact solution for the metric, $\d s^2=-(c+\tanh \lambda x)\d t^2+ \d x^2/(c+\tanh {\lambda} x)$, parametrized by $c$. For $c\in(-1,1)$, the solution presents an event horizon but no singularity. Because of the kink profile for the metric components appearing in the solution, we refer to the spacetime described by the metric as a {\it gravitational domain wall} with the wall simply being the event horizon and separating two asymptotically Minkowskian spacetimes. The global causal structure for such an object is studied via coordinate extension and the thermodynamical quantities are computed. Only when $c\in(-1,0]$ are the entropy and energy non-negative.