Thermodynamic Properties of Static and Rotating Unparticle Black Holes

TL;DR

This paper derives thermodynamic properties of static and rotating unparticle black holes, revealing phase transitions, stability regions, and horizon fractalization, and compares these features to black holes with quintessence.

Contribution

It provides the first analytical expressions for thermodynamics of scalar, tensor, and vector unparticle black holes, including rotating solutions and their unique horizon structures.

Findings

Identification of phase transitions in vector unparticle black holes.

Existence of thermodynamically stable regions for certain parameters.

Discovery of horizon fractalization dependent on rotation and angle.

Abstract

In this paper we find analytical expressions for thermodynamic quantities of scalar (tensor) and vector unparticle static black holes. We also find rotating solutions to these systems and analyse their thermodynamics. First we consider the static case with a spherically symmetric source for both the vector and scalar (tensor) unparticles. We obtain thus analytical expressions to the principal thermodynamic quantities: Hawking temperature, entropy, heat capacity and free energy. For the scalar (tensor) case we find that the black hole presents a residual value for the entropy when its radius goes to zero but the other thermodynamic quantities give, for any horizon radius, a thermodynamically unstable behavior similar to the standard black hole. For the vector case we find a richer structure in the region in which the horizon radius is less than the characteristic length of the unparticle theory. We identify a phase transition and a region where the black hole can be thermodynamically stable. Following, we show that the mentioned modifications in the standard gravity are formally similar to those ones present in the black holes with quintessence. With this we also show, notwithstanding, that the unparticles cannot be a source of quintessence. By using this similarity we find two different rotating solutions to the unparticle black holes based on works by Ghosh and Toshmatov {\it et al}. For both cases we compute the Hawking temperature and in the ungravity dominated regime we find, as in the static cases, a fractalization of the event horizon. For the Gosh-like solution the fractal dimension depends on the polar angle and on the rotation of the source. For the Toshmatov-like one it is equal to the static case and therefore the fractalization is not dependent on the rotation of the source.