Bopp-Podolsky black holes and the no-hair theorem

Abstract

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 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's one. Thus, in light of 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.

9 pages, updated to match published version

References in corpus (4)

• Superradiant Instability and Backreaction of Massive Vector Fields around Kerr Black Holes
• Classical and quantum stability of higher-derivative dynamics
• Path Integral Quantization of Generalized Quantum Electrodynamics
• Self-interaction in the Bopp-Podolsky electrodynamics: Spacetimes with angular defects

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• Second gradient electrodynamics: a non-singular relativistic field theory
• Conundrum of regular black holes with nonlinear electromagnetic fields
• High-derivatives and massive electromagnetic models in the Lemaitre-Tolman-Bondi spacetime
• Compatibility of the Dimensional Reduction and Variation Procedures for a Quadratic Curvature Model with a Kaluza-Klein Ansatz