Static Charged Black Holes in $(2+1)$ Dimensional Dilaton Gravity

TL;DR

This paper presents a family of static charged black hole solutions in (2+1)-dimensional dilaton gravity, analyzing their causal structures, thermodynamics, and special cases including solutions with cosmological horizons and tachyonic dilatons.

Contribution

It introduces a new family of static charged black hole solutions in (2+1)D dilaton gravity with detailed analysis of their properties and thermodynamics.

Findings

One black hole has thermodynamics similar to 3+1 Schwarzschild black hole.

Solutions with cosmological horizons are identified and discussed.

A class of black holes with tachyonic dilaton fields is briefly explored.

Abstract

A one parameter family of static charged black hole solutions in $(2+1)$-dimensional general relativity minimally coupled to a dilaton $\phi\propto ln({r\over\beta})$ with a potential term $e^{b\phi}\Lambda$ is obtained. Their causal strutures are investigated, and thermodynamical temperature and entropy are computed. One particular black hole in the family has the same thermodynamical properties as the Schwarzschild black hole in $3+1$ dimensions. Solutions with cosmological horizons are also discussed. Finally, a class of black holes arising from the dilaton with a negative kinetic term (tachyon) is briefly discussed.