Thermodynamics of Black Holes in Schroedinger Space

TL;DR

This paper investigates the thermodynamics of black holes in Schroedinger space, deriving their actions, analyzing phase transitions, and comparing with AdS black holes, revealing similar thermodynamic properties and phase behavior.

Contribution

It introduces a novel regularization method for black hole thermodynamics in Schroedinger space and applies it to derive phase diagrams and compare with AdS solutions.

Findings

Actions match AdS counterparts for black solutions

Phase diagram shows Hawking-Page transition and instabilities

Regularization method correctly reproduces known thermodynamics

Abstract

A black hole and a black hyperboloid solutions in the space with the Schroedinger isometries are presented and their thermodynamics is examined. The on-shell action is obtained by the difference between the extremal and non-extremal ones with the unusual matching of the boundary metrics. This regularization method is first applied to the black brane solution in the space of the Schroedinger symmetry and shown to correctly reproduce the known thermodynamics. The actions of the black solutions all turn out to be the same as the AdS counterparts. The phase diagram of the black hole system is obtained in the parameter space of the temperature and chemical potential and the diagram contains the Hawking-Page phase transition and instability lines.