Novel five-dimensional rotating Lifshitz black holes with electric and axionic charges

Abstract: In the present paper, we construct a new family of exact charged and rotating asymptotically Lifshitz black hole solutions in five dimensions. The spacetime solves Einstein equations coupled to a dilaton, two Abelian gauge fields, and axionic scalars supplemented by two generalized Chern-Simons terms. This configuration is characterized by a range of the free dynamical exponent $z$ and possesses nontrivial thermodynamical parameters, where we verify the first law of black hole thermodynamics and derive the corresponding Smarr relation. Motivated by applications to gauge/gravity duality, we then investigate a holographic superconductor in the rotating Lifshitz background. We study the condensation of the scalar operator and the AC conductivity of the dual system. These results show that increasing the rotation parameter suppresses the condensate and weakens the superconducting phase, while increasing the dynamical critical exponent enhances the superconducting order. To the best of our knowledge, the solutions presented here are the first to demonstrate five-dimensional rotating Lifshitz black holes supported by both electric and axionic charges. This opens up a new avenue to investigate non-relativistic holography beyond static backgrounds.