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Dilaton gravity approach to three-dimensional Lifshitz black hole

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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.

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Authors and Affiliations

  1. Institute of Basic Science and School of Computer Aided Science, Inje University, Gimhae, 621-749, Korea

    Yun Soo Myung & Yong-Wan Kim

  2. Department of Physics and Center for Quantum Spacetime, and WCU-SSME Program Division, Sogang University, Seoul, 121-742, Korea

    Young-Jai Park

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  1. Yun Soo Myung
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  2. Yong-Wan Kim
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Correspondence to Yong-Wan Kim.

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Myung, Y.S., Kim, YW. & Park, YJ. Dilaton gravity approach to three-dimensional Lifshitz black hole. Eur. Phys. J. C 70, 335–340 (2010). https://doi.org/10.1140/epjc/s10052-010-1460-x

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  • DOI: https://doi.org/10.1140/epjc/s10052-010-1460-x

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