Some exact solutions of all f(Ricci) theories in three dimensions

TL;DR

This paper derives exact constant scalar curvature solutions in all three-dimensional higher curvature gravity theories based on the Ricci tensor, extending known solutions from topologically massive and new massive gravity.

Contribution

It provides a unified method to find exact solutions in all f(Ricci) theories in three dimensions, including quadratic, cubic, and Born-Infeld extensions.

Findings

Found constant scalar curvature Type-N and Type-D solutions.

Demonstrated inheritance of solutions from known massive gravity models.

Extended solutions to specific higher curvature theories.

Abstract

We find constant scalar curvature Type-N and Type-D solutions in all higher curvature gravity theories with actions of the form f(Ricci) that are built on the Ricci tensor, but not on its derivatives. In our construction, these higher derivative theories inherit some of the previously studied solutions of the cosmological topologically massive gravity and the new massive gravity field equations, once the parameters of the theories are adjusted. Besides the generic higher curvature theory, we have considered in some detail the examples of the quadratic curvature theory, the cubic curvature theory, and the Born-Infeld extension of the new massive gravity.