Eur. Phys. J. C 70, 335-340 (2010)
https://doi.org/10.1140/epjc/s10052-010-1460-x

Dilaton gravity approach to three-dimensional Lifshitz black hole

¹ Institute of Basic Science and School of Computer Aided Science, Inje University, Gimhae, 621-749, Korea
² Department of Physics and Center for Quantum Spacetime, and WCU-SSME Program Division, Sogang University, Seoul, 121-742, Korea

ywkim65@gmail.com

Received: 30 June 2010
Revised: 15 September 2010
Published online: 15 October 2010

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, Bekenstein–Hawking entropy, and free energy.