# 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