Non-abelian (hyperscaling violating) Lifshitz black holes in general dimensions

We consider Einstein gravities coupled to a cosmological constant and multiple SU(2)SU(2) Yang–Mills fields in general dimensions and find that the theories admit colored Lifshitz solutions with dynamic exponents z>1z>1. We also introduce a Maxwell field and construct exact electric charged black holes that asymptote to the z=D−1z=D−1 colored Lifshitz spacetimes and analyze their thermodynamical first law. Furthermore, we introduce a dilaton to the system and construct Lifshitz spacetimes with hyperscaling violations. After turning on the Maxwell field, we obtain a class of hyperscaling violating Lifshitz black holes when θ=2D−2[z−(D−1)].