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arXiv · 1403.5985

Nonlinearly charged Lifshitz black holes for any exponent $z>1$

Abigail Alvarez·Eloy Ayón-Beato·Hernán A. González·Mokhtar Hassaïne
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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 $(\mathcal{H},P)$-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.

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Abigail Alvarez, Eloy Ayón-Beato, Hernán A. González, Mokhtar Hassaïne. 2014-03-24. Nonlinearly charged Lifshitz black holes for any exponent $z>1$. https://doi.org/10.1007/jhep06(2014)041

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