Strategy to Construct Exact Solutions in Einstein-Scalar Gravities

TL;DR

The paper introduces a new method for constructing exact solutions in Einstein-scalar gravities by leveraging symmetries of the equations of motion, enabling the derivation of solutions including black holes and their thermodynamics.

Contribution

A novel strategy that uses EOM symmetries to systematically generate exact Einstein-scalar solutions, extending to higher dimensions and various metrics.

Findings

Constructed exact circular solutions in 3D gravity including HMTZ black holes.

Demonstrated the method's applicability to higher dimensions and different metrics.

Analyzed thermodynamics of the obtained solutions.

Abstract

In this article we propose a new efficient strategy to construct exact solutions of Einstein gravities with a minimally coupled self-interacting scalar field. The strategy is to use the symmetry of the equations of motion (EOMs) to give a proper ansatz for scalar field first, then derive the metric and the corresponding scalar potential later. Using this strategy we give a simple example of constructing exact circular solutions in three dimensional gravities, these solutions contain the HMTZ black holes as a special case and some other new solutions. We also talk about thermodynamics of these exact solutions. This strategy also works for other metrics and in higher dimensional spacetime if their EOMs admit a scalar invariance.