Spherically symmetric black holes with electric and magnetic charge in extended gravity: physical properties, causal str
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Regular Article - Theoretical Physics
Spherically symmetric black holes with electric and magnetic charge in extended gravity: physical properties, causal structure, and stability analysis in Einstein’s and Jordan’s frames E. Elizalde1,a , G. G. L. Nashed2,b , S. Nojiri3,c , S. D. Odintsov1,4,5,d 1
Institut de Ciències de l’Espai (ICE-CSIC/IEEC), Campus UAB, c. Can Magrans s/n, 08193 Barcelona, Spain Centre for Theoretical Physics, The British University in Egypt, El Sherouk City 11837, Egypt 3 Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Department of Physics, Nagoya University, Nagoya 464-8602, Japan 4 Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain 5 Tomsk State Pedagogical University, 634061 Tomsk, Russia
2
Received: 22 December 2019 / Accepted: 23 January 2020 © The Author(s) 2020
Abstract Novel static black hole solutions with electric and magnetic charges are derived for the class of modified √ gravities: f (R) = R + 2β R, with or without a cosmological constant. The new black holes behave asymptotically as flat or (A)dS space-times with a dynamical value of the 2 , respecRicci scalar given by R = r12 and R = 8r r+1 2 tively. They are characterized by three parameters, namely their mass and electric and magnetic charges, and constitute black hole solutions different from those in Einstein’s general relativity. Their singularities are studied by obtaining the Kretschmann scalar and Ricci tensor, which shows a dependence on the parameter β that is not permitted to be zero. A conformal transformation is used to display the black holes in Einstein’s frame and check if its physical behavior is changed w.r.t. the Jordan one. To this end, thermodynamical quantities, as the entropy, Hawking temperature, quasi-local energy, and the Gibbs free energy are calculated to investigate the thermal stability of the solutions. Also, the casual structure of the new black holes is studied, and a stability analysis is performed in both frames using the odd perturbations technique and the study of the geodesic deviation. It is concluded that, generically, there is coincidence of the physical properties of the novel black holes in both frames, although this turns not to be the case for the Hawking temperature.
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1 Introduction The discovery of gravitational waves (GW) has shed light on a new possibility to probe the laws of physics in strong gravitational fields [1]. General relativity (GR) has been confirmed to a very good precision on weak gravitational field backgrounds [2]; however, the precise form of the anticipated, necessary modification of GR to deal with strong gravitational fields is not confirmed yet, although different possibilities have been proposed. The discovery of GW definitely provides an excellent chance to test those modified gravity theories in the strong gravitational fields of black
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