Thermodynamics of non-linearly charged Anti-de Sitter black holes in four-dimensional Critical Gravity

Abstract

In this work, we provide new examples of Anti-de Sitter black holes with a planar base manifold in four-dimensional Critical Gravity by considering nonlinear electrodynamics as a matter source. We find a general solution characterized by the presence of only one integration constant where, for a suitable election of coupling constants, we can show the existence of one or more horizons. Additionally, we compute its non-null thermodynamical quantities through a variety of techniques, testing the validity of the first law of thermodynamics as well as a Smarr formula. Finally, we analyze the local thermodynamical stability of the solutions. To our knowledge, these charged configurations are the first example with Critical Gravity where their thermodynamical quantities are not zero. * abialvarez-at-uv.mx † mbravo-at-ucm.cl ‡ mjuarez-at-astate.edu § gvelazquez-at-astate.edu

Non-linear charged planar black holes in four-dimensional Scalar-Gauss-Bonnet theories

“…1, where this charged configuration is simultaneously locally stable under thermal and electrical fluctuations. This feature has been obtained previously for Critical Gravity black holes [85], not so for the non-linear charged configurations [67] dressed with a scalar field non-minimally coupled, where this solution enjoys local stability under thermal fluctuations but not under electrical ones.…”

“…We immediately note that, in order to obtain a non-null mass for the black hole, we need as a minimum to turn on the scalar field ψ and to receive both contributions from our structural function (5). This is, in turn, the same observation that led to nonzero thermodynamic quantities in four-dimensional Critical Gravity [85] as well as the Einstein-Proca model [82,83], and that highlights the importance of the choice of the NLE as a matter source.…”

“…On the other hand on the electromagnetic side, recently, there has been a growing interest in a different nonlinear electrodynamics source, characterized by the antisymmetric conjugate tensor P µν (the Plebański tensor), and a structure-function H(P ). This choice of a matter source has allowed obtaining regular black holes solutions [74][75][76][77][78], an exact solution of a massive, electromagnetically charged and rotating configuration [79][80][81], black holes with non-standard asymptotic behavior [82,83], slowly rotating black holes [84], and the construction of black holes within the context of Critical Gravity [85]. A hint to the present work is taken from this last reference.…”

“…A complete analysis of this statement is performed through Noether-Wald charges in [87,88], also for its sixdimensional analog. The introduction of the NLE source in [85] generates a fruitful interaction with all the integration constants, leading to a stable black hole with non-null mass, entropy, and electric charge.…”