Hyperscaling violating black holes with spherical and hyperbolic horizons

TL;DR

This paper introduces a new family of charged black holes with hyperscaling violation and various horizon topologies, analyzing their thermodynamics and phase transitions across different parameters.

Contribution

It provides explicit analytic solutions for hyperscaling violating black holes with spherical and hyperbolic horizons in a generalized Einstein-Maxwell-Dilaton framework.

Findings

Hyperbolic solutions are valid only for specific $z$ and $ heta$ ranges.

Phase transitions occur only for spherical black holes with $1 \,\leq\, z \leq 2$.

Solutions extend understanding of black hole thermodynamics in hyperscaling violating backgrounds.

Abstract

We present a new family of charged black holes with hyperscaling violating asymptotics and non-trivial horizon topology, for arbitrary Lifshitz exponent $z$ and hyperscaling violation parameter $\theta$. They are $(d+2)$-dimensional analytic solutions to a generalized Einstein-Maxwell-Dilaton theory with an additional vector field supporting spherical or hyperbolic horizons. The hyperbolic solutions are only consistent with the null energy condition for $1 \le z < 2$ and $\theta = d(z-1)$, which explains why they are absent in the pure Lifshitz case. We further study the (extended) thermodynamics of these black holes, both in the fixed charge and fixed potential ensemble, and find that phase transitions only occur for spherical black holes with $1 \le z \le 2$ and any $\theta$.