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Charged Lifshitz black holes for the Einstein-Proca-Maxwell system with anegative cosmological constant in arbitrary dimension $D$ are known only if thedynamical critical exponent is fixed as $z=2(D-2)$. In the present work, weshow that these configurations can be extended to much more general chargedblack 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 definedin the more general, but less known, so-called $(\mathcal{H},P)$-formalism andobtain a family of charged black hole solutions depending on two parameters. Wealso remark that the value of the dynamical exponent $z=D-2$ turns out to becritical in the sense that it yields asymptotically Lifshitz black holes withlogarithmic decay supported by a particular logarithmic electrodynamics. Allthese configurations include extremal Lifshitz black holes. Charged topologicalLifshitz black holes are also shown to emerge by slightly generalizing theproposed electrodynamics.

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