AdS Black Hole with Phantom Scalar Field

TL;DR

This paper introduces an AdS black hole solution with a phantom scalar field, analyzes its thermodynamics showing similarities to Schwarzschild black holes, and explores entanglement entropy behavior in the dual field theory.

Contribution

It presents a new AdS black hole solution with phantom scalar fields and studies its thermodynamics and entanglement entropy, revealing phase transition characteristics.

Findings

Existence of a minimal temperature for the black hole

Thermodynamically stable large black holes

Entanglement entropy behavior mirrors thermodynamic entropy

Abstract

In this paper, 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 $y$, and 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 same as those of AdS Schwarzschild black hole. Namely there exists a minimal temperature, 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 spacetime 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.