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We present a new family of charged black holes with hyperscaling violatingasymptotics and non-trivial horizon topology, for arbitrary Lifshitz exponent$z$ and hyperscaling violation parameter $\theta$. They are $(d+2)$-dimensionalanalytic solutions to a generalized Einstein-Maxwell-Dilaton theory with anadditional vector field supporting spherical or hyperbolic horizons. Thehyperbolic 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 thepure Lifshitz case. We further study the (extended) thermodynamics of theseblack holes, both in the fixed charge and fixed potential ensemble, and findthat phase transitions only occur for spherical black holes with $1 \le z \le2$ and any $\theta$.

Hyperscaling violating black holes with spherical and hyperbolic horizons