Dilaton gravity approach to three dimensional Lifshitz black hole

TL;DR

This paper uses a dimensional reduction to analyze a three-dimensional Lifshitz black hole within a two-dimensional dilaton gravity framework, enabling easier computation of thermodynamic properties.

Contribution

It introduces a method to study three-dimensional Lifshitz black holes via two-dimensional dilaton gravity, simplifying thermodynamic analysis.

Findings

Thermodynamic quantities like temperature, mass, and entropy are derived from the two-dimensional model.

The same Lifshitz black hole solution appears in both three and two dimensions.

The approach confirms the consistency of thermodynamic properties across dimensions.

Abstract

The z=3 Lifshitz black hole is an exact black hole solution to the new massive gravity in three dimensions. In order to understand this black hole clearly, we perform a dimensional reduction to two dimensional dilaton gravity by utilizing the circular symmetry. Considering the linear dilaton, we find the same Lifshitz black hole in two dimensions. This implies that all thermodynamic quantities of the z=3 Lifshitz black hole could be obtained from its corresponding black hole in two dimensions. As a result, we derive the temperature, mass, heat capacity, Bekesnstein-Hawking entropy, and free energy.