Thermodynamics of string black hole with hyperscaling violation

TL;DR

This paper constructs hyperscaling-violating string black hole solutions using Null-Melvin-Twist and KK-reduction, analyzing their thermodynamics and showing the absence of Hawking-Page phase transition.

Contribution

It introduces a method to generate hyperscaling-violating string solutions and studies their thermodynamics, revealing the lack of phase transition for specific hyperscaling parameters.

Findings

Free energy is always negative for hyperscaling violation with θ=d/2.

No Hawking-Page phase transition occurs in these solutions.

The system remains in thermal radiation state without black hole formation.

Abstract

In this paper, we start with black brane and construct specific space-time which violates hyperscaling. In order to obtain the string solution we apply Null-Melvin-Twist and $KK$-reduction. By using the difference action method we study thermodynamics of system to obtain Hawking-Page phase transition. In order to have hyperscaling violation we need to consider $\theta=\frac{d}{2}.$ In that case the free energy $F$ is always negative and our solution is thermal radiation without a black hole. Therefore we find that there is not any Hawking-Page transition. Also, we discuss the stability of system and all thermodynamical quantities.