Spherically symmetric solutions of Einstein + non-polynomial gravities

TL;DR

This paper derives static spherically symmetric solutions in modified gravity theories that extend Einstein's General Relativity, resulting in novel geometries with horizons and singularities, and explores their properties across various dimensions and additional physical terms.

Contribution

It introduces a class of non-polynomial gravity models that alter the Schwarzschild solutions, maintaining first-order equations and extending to higher dimensions with additional physical effects.

Findings

Solutions generally have horizons and singularities.

One model uniquely forbids spherical symmetry.

Extensions include cosmological constant, Maxwell, and Gauss-Bonnet terms.

Abstract

We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to maintain the (first) derivative order of the Einstein equations in Schwarzschild gauge. Generically, the solutions exhibit both horizons and a singularity at the origin, except for one model that forbids spherical symmetry altogether. Extensions to arbitrary dimension with a cosmological constant, Maxwell source and Gauss-Bonnet terms are also considered.