A special class of solutions in $F(R)$-gravity

TL;DR

This paper explores a special class of vacuum $F(R)$-gravity models where solutions with constant Ricci scalar trivially satisfy field equations, investigating static, spherically symmetric solutions including black holes, wormholes, and galaxy rotation curves.

Contribution

It identifies and analyzes a specific class of $F(R)$-gravity solutions beyond cosmology, focusing on static, spherically symmetric spacetimes such as black holes and wormholes.

Findings

Trivial satisfaction of field equations for constant Ricci scalar in this class.

Existence of black hole and wormhole solutions within this $F(R)$-gravity class.

Potential explanations for galaxy rotation curves without dark matter.

Abstract

We consider a special class of vacuum $F(R)$-modified gravity models. The form of their Lagrangian is such that the field equations are trivially satisfied when the Ricci scalar is constant. There are many interesting $F(R)$-models for inflation and dark energy that fall in this class. However, little is known outside the domain of cosmology therefore we aim to explore the class of solutions that are static and spherically symmetric. After some general considerations, we investigate in more detail black hole solutions, traversable wormhole metrics and, finally, configurations that can match the anomalous rotation curves of galaxies.