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

Marco Calzà,Lorenzo Sebastiani,Massimiliano Rinaldi

doi:10.1140/epjc/s10052-018-5681-8

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.

Highlights

In the context of cosmology, F(R) gravity has raised a lot of interest as it represents a promising alternative to scalar inflation and/or dark energy
We investigate in more detail black hole solutions, traversable wormhole metrics and, configurations that can match the anomalous rotation curves of galaxies
We consider a special class of F(R)-gravity models whose Lagrangians satisfy two constraints, namely F(R0) = 0 and FR(R0) = 0, where FR denotes the first derivative of F(R) with respect to R and R0 is a constant value for the Ricci scalar

Summary

Introduction

In the context of cosmology, F(R) gravity has raised a lot of interest as it represents a promising alternative to scalar inflation and/or dark energy. We consider a special class of F(R)-gravity models whose Lagrangians satisfy two constraints, namely F(R0) = 0 and FR(R0) = 0, where FR denotes the first derivative of F(R) with respect to R and R0 is a constant (eventually vanishing) value for the Ricci scalar. Note that General Relativity does not belong to this class of theories since its vacuum equations of motion are identically satisfied by any metric with R = 0 but FR(R) = 1. We focus on the class of static and spherically symmetric solutions with constant (or vanishing) Ricci scalar that satisfy the general vacuum F(R) equations of motion.

The model Ansatz

Traversable wormholes

Rotation curves of galaxies