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

In this work, we construct a new family of exact five-dimensional charged and rotating asymptotically Lifshitz black holes. 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. As an application of this new gravitational background, 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, these solutions provide the first explicit family of five-dimensional rotating Lifshitz black holes supported simultaneously by electric and axionic charges.