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Home > Advances in High Energy Physics (Hindawi) > AdS Black Hole with Phantom Scalar Field |

Li, Zhonghua (Institute of Theoretical Physics, China West Normal University, Nanchong, Sichuan 637002, China) ; Zhang, Limei (College of Physics and Space Science, China West Normal University, Nanchong, Sichuan 637002, China) ; Zeng, Xiaoxiong (Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China)

15 October 2017

**Abstract: **We present an AdS black hole solution with Ricci flat horizon in Einstein-phantom scalar theory. The phantom scalar fields just depend on the transverse coordinates $x$ and $y$ , which are parameterized by the parameter $\alpha $ . We study the thermodynamics of the AdS phantom black hole. Although its horizon is a Ricci flat Euclidean space, we find that the thermodynamical properties of the black hole solution are qualitatively the same as those of AdS Schwarzschild black hole. Namely, there exists a minimal temperature and the large black hole is thermodynamically stable, while the smaller one is unstable, so there is a so-called Hawking-Page phase transition between the large black hole and the thermal gas solution in the AdS space-time in Poincare coordinates. We also calculate the entanglement entropy for a strip geometry dual to the AdS phantom black holes and find that the behavior of the entanglement entropy is qualitatively the same as that of the black hole thermodynamical entropy.

**Published in: ****Advances in High Energy Physics 2017 (2017) 4940187**
**Published by: **Hindawi

**DOI: **10.1155/2017/4940187

**arXiv: **1707.04429

**License: **CC-BY-3.0