Generalisation for regular black holes on general relativity to f(R) gravity

Manuel E. Rodrigues,Júlio C. Fabris,Glauber T. Marques,Ednaldo L. B. Junior

doi:10.1140/epjc/s10052-016-4085-x

Abstract

In this paper, we determine regular black hole solutions using a very general $f(R)$ theory, coupled to a non-linear electromagnetic field given by a Lagrangian $\mathcal{L}_{NED}$. The functions $f(R)$ and $\mathcal{L}_{NED}$ are left in principle unspecified. Instead, the model is constructed through a choice of the mass function $M(r)$ presented in the metric coefficients. Solutions which have a regular behaviour of the geometric invariants are found. These solutions have two horizons, the event horizon and the Cauchy horizon. All energy conditions are satisfied in the whole space-time, except the strong energy condition (SEC) which is violated near the Cauchy horizon.

Highlights

The most popular, and most simple, candidate for dark energy is the cosmological constant
We have investigated the existence of regular black hole structures for a general f (R) theory, sourced by non-linear electromagnetic terms expressed by the Lagrangian LNED
Our approach follows very closely the one employed in Ref. [62]: instead of choosing specific forms for the f (R) and LNED functions, the approach consists in expressing the metric in terms of a mass function M(r ) and to choose a mass function that satisfies some requirements

Summary

Introduction

The most popular, and most simple, candidate for dark energy is the cosmological constant. [63], with GR theory coupled to a nonlinear electromagnetic field, in order to satisfy some requirements, like to avoid violation of the weak energy condition (WEC) and to have the Reissner–Nordström asymptotic limit: the mass function M(r ) given in Ref. We call to attention that the effective energy–momentum tensor in (23) is equal to the Einstein tensor, which is in the left hand side of that equation This means that the energy conditions are related only to the type of geometry for which the solution is written, and they can be the same for two different theories as, in the present case, for GR and f (R) gravity. We will use a specific model for the general mass function M(r ), coming from GR, in order to obtain a generalisation of this class of solutions

New regular black hole solutions

Conclusion