Nonlinearly charged Lifshitz black holes for any exponent z > 1

Abstract

Charged Lifshitz black holes for the Einstein-Proca-Maxwell system with a negative cosmological constant in arbitrary dimension D are known only if the dynamical critical exponent is fixed as z = 2(D − 2). In the present work, we show that these configurations can be extended to much more general charged black holes which in addition exist for any value of the dynamical exponent z > 1 by considering a nonlinear electrodynamics instead of the Maxwell theory. More precisely, we introduce a two-parametric nonlinear electrodynamics defined in the more general, but less known, so-called (H, P )-formalism and obtain a family of charged black hole solutions depending on two parameters. We also remark that the value of the dynamical exponent z = D − 2 turns out to be critical in the sense that it yields asymptotically Lifshitz black holes with logarithmic decay supported by a particular logarithmic electrodynamics. All these configurations include extremal Lifshitz black holes. Charged topological Lifshitz black holes are also shown to emerge by slightly generalizing the proposed electrodynamics.

Static and rotating solutions for vector-Galileon theories

“…The interest for such models has started with the pioneering work of Born and Infeld [53] whose main motivation was to modify the standard Maxwell theory in order to eliminate the problem of infinite energy of the electron. Nonlinear electrodynamics is also crucial for the construction of regular black holes [54] and for anisotropic black hole solutions [55]. In addition, owing to their peculiar thermodynamics properties, nonlinear electrodynamic models have also attracted a lot attention from the physics community [56].…”

Cardy formula for charged black holes with anisotropic scaling

“…For this solution, the uncharged Abelian field F (1)rt , the dilaton, the cosmological constant and the coupling constants are given by the same expressions than in the linear case, see (20b), (20d) and (21). The only changes are concerned with the charged Abelian gauge field F (2)rt and the coupling constant λ 2 which now take the following forms…”

“…This problem has a certain interest since electrically charged Lifshitz black holes have also be found in the current literature, see e. g. [18][19][20][21][22][23]. Such examples occur for example in the case of Einstein gravity with a source given by a ProcaMaxwell action [20] or in presence of N −Abelians U (1) fields with a dilaton [24] as well as in the case of nonlinear electrodynamics [21,22]. In all these examples, a Smarr formula generalizing the expression (4) can be derived and, is generically written as [16] …”

Quasinormal modes of four-dimensional topological nonlinear charged Lifshitz black holes

“…The solution to the problem of constructing charged asymptotically Lifshitz black holes was solved adding the Maxwell action to the described Proca system [14]. In this work, only configurations for the dynamical exponent z = 2(D − 2) were found; however, in [15] these configurations were extended to a much more general charged black holes for any value of the dynamical exponent z > 1 by considering nonlinear electrodynamics. Very recently, in [16], analytic topological Lifshitz black holes with constant curvature horizon in the presence of a powerlaw Maxwell field in four and higher dimensions were constructed.…”