https://doi.org/10.1140/epjc/s10052-018-5525-6
Regular Article - Theoretical Physics
Bopp–Podolsky black holes and the no-hair theorem
1
Department of Physics, McGill University, Ernest Rutherford Physics Building, 3600 University Street, Montreal, QC, H3A 2T8, Canada
2
Instituto de Ciência e Tecnologia, Universidade Federal de Alfenas, Rod. José Aurélio Vilela (BR 267), Km 533, n. 11999, Poços de Caldas, MG, CEP 37701-970, Brazil
3
Instituto de Física Teórica, Universidade Estadual Paulista, Rua Bento Teobaldo Ferraz 271 Bloco II, P.O. Box 70532-2, São Paulo, SP, CEP 01156-970, Brazil
4
Escola de Ciência e Tecnologia, Universidade Federal do Rio Grande do Norte, Campus Universitário, s/n-Lagoa Nova, Natal, RN, CEP 59078-970, Brazil
5
Departamento de Física, Instituto Tecnológico de Aeronáutica, Praça Mal. Eduardo Gomes 50, São José dos Campos, SP, CEP 12228-900, Brazil
* e-mail: leogmedeiros@gmail.com
Received:
6
November
2017
Accepted:
4
January
2018
Published online:
19
January
2018
Bopp–Podolsky electrodynamics is generalized to curved space-times. The equations of motion are written for the case of static spherically symmetric black holes and their exterior solutions are analyzed using Bekenstein’s method. It is shown that the solutions split up into two parts, namely a non-homogeneous (asymptotically massless) regime and a homogeneous (asymptotically massive) sector which is null outside the event horizon. In addition, in the simplest approach to Bopp–Podolsky black holes, the non-homogeneous solutions are found to be Maxwell’s solutions leading to a Reissner–Nordström black hole. It is also demonstrated that the only exterior solution consistent with the weak and null energy conditions is the Maxwell one. Thus, in the light of the energy conditions, it is concluded that only Maxwell modes propagate outside the horizon and, therefore, the no-hair theorem is satisfied in the case of Bopp–Podolsky fields in spherically symmetric space-times.
© The Author(s), 2018
