(Anti-) de Sitter electrically charged black-hole solutions in higher-derivative gravity

Abstract

In this paper, static electrically charged black hole solutions with cosmological constant are investigated in an Einstein-Hilbert theory of gravity with additional quadratic curvature terms. Beside the analytic Schwarzschild (Anti-) de Sitter solutions, non-Schwarzschild (Anti-) de Sitter solutions are also obtained numerically by employing the shooting method. The results show that there exist two groups of asymptotically (Anti-) de Sitter spacetimes for both charged and uncharged black holes. In particular, it was found that for uncharged black holes the first group can be reduced to the Schwarzschild (Anti-) de Sitter solution, while the second group is intrinsically different from a Schwarzschild (Anti-) de Sitter solution even when the charge and the cosmological constant become zero.PACS numbers: 04.70.Bw, 04.25.dg, 04.60.-m Though Einstein's general relativity has been extensively tested at the highest achievable experimental precision up to date, gravity is not a renormalizable quantum field theory from the theoretical viewpoint. A possible attempt to solve the problem of the non-renormalizability of general relativity is to include higher-order corrections that become important at higher energy [1]. In this context, general relativity can be viewed as an effective low-energy field theory, which is understood to be largely independent of the details in higher energy scales. It can be shown when all possible quadratic curvature invariants are added to the Einstein-Hilbert action, a renormalizable theory is achieved at the cost of the presence of the ghost modes [2]. Thus the study of the properties of such higher-derivative gravity could shed light on the ongoing efforts to understand the nature of gravity.In order to better understand such a new theory of gravity, it seems of considerable interest to investigate the behaviour of black hole solutions, since they are fundamental objects in general relativity. Such studies have also been performed in other theories of gravity containing higher order curvature corrections with well defined coefficients, such as Lovelock theory [3]. Moreover, the question of stability of charged Black Holes is relevant and has been intensively studied recently in recent years [4,5].Recently, Lü et. al found, numerically, a non-Schwarzschild solution in a theory of gravity with a quadratic Weyl scalar on action [6,7], and revealed that this higher-derivative gravity possesses additional static spherically symmetric black hole solution comparing to Einstein's general relativity. We also showed in [8] that electrically charged static solutions in this theory are also characterized by two groups of solutions. These solutions reduce respectively to Schwarzschild black hole and non-Schwarzschild black hole solutions, when the charge of the black hole goes to zero. Surprisingly the Reissner-Nordström metric is not a solution of the field equations when the coefficients of the higher-derivative terms do not vanish.Being first introduced by Einstein to describe a static universe and ...

Charged black holes in the Einstein-Maxwell-Weyl gravity

“…Another interesting possibility is (Anti-) de Sitter charged black hole solutions in Einstein-Maxwell-Weyl gravity. They have shown in the Einstein-Hilbert theory of gravity with additional quadratic curvature terms [17]. Beside the analytic Schwarzschild (Anti-) de Sitter solutions, two groups of non-Schwarzschild (Anti-) de Sitter solutions were also obtained numerically.…”

Black hole with primary scalar hair in Einstein-Weyl-Maxwell conformal scalar theory

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Quadratic gravity and conformally coupled scalar fields

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