Eur. Phys. J. C (2016) 76: 250
https://doi.org/10.1140/epjc/s10052-016-4085-x

Regular Article - Theoretical Physics

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

¹ Faculdade de Ciências Exatas e Tecnologia, Universidade Federal do Pará Campus Universitário de Abaetetuba, CEP 68440-000, Abaetetuba, Pará, Brazil
² Faculdade de Física, PPGF, Universidade Federal do Pará, 66075-110, Belém, Pará, Brazil
³ Faculdade de Engenharia da Computação, Universidade Federal do Pará, Campus Universitário de Tucuruí, CEP 68464-000, Tucuruí, Pará, Brazil
⁴ Universidade Federal Rural da Amazônia ICIBE - LASIC, Av. Presidente Tancredo Neves 2501, CEP 66077-901, Belém, PA, Brazil
⁵ Universidade Federal do Espírito Santo, CEP 29075-910, Vitória, ES, Brazil
⁶ National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409, Russia

^* e-mail: fabris@pq.cnpq.br

Received: 6 January 2016
Accepted: 14 April 2016
Published online: 2 May 2016

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 . The functions f(R) and are in principle left 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. We present also a new theorem related to the energy conditions in f(R) gravity, re-obtaining the well-known conditions in the context of general relativity when the geometry of the solution is the same.