Scaling symmetry and scalar hairy Lifshitz black holes

TL;DR

This paper explores the scaling symmetry in Lifshitz black holes with scalar hair, deriving conserved charges and generalized Smarr relations, including new relations for Lifshitz black holes with scalar hair across multiple dimensions.

Contribution

It introduces a method to derive conserved charges and Smarr relations for Lifshitz black holes with scalar hair using scaling symmetry, extending known results to new cases.

Findings

Derived conserved charge from scaling symmetry.

Established generalized Smarr relations for various black holes.

Discovered new Smarr relation for Lifshitz black holes with scalar hair.

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.