Scaling symmetry and scalar hairy Lifshitz black holes

Abstract

Abstract: By utilizing the scaling symmetry of the reduced action for planar black holes, we obtain the corresponding conserved charge. We use the conserved charge to find the generalized Smarr relation of static hairy planar black holes in various dimensions. Our results not only reproduce the relation in the various known cases but also give the new relation in the Lifshitz planar black holes with the scalar hair.