Critical behavior for the dilaton black holes

TL;DR

This paper investigates the critical phenomena and phase transitions in dilaton black holes and black p-branes, revealing critical points at extremal limits and deriving critical exponents consistent with scaling laws.

Contribution

It provides a detailed analysis of thermodynamic fluctuations and phase transitions in dilaton black holes, highlighting the critical behavior at extremal limits and calculating associated critical exponents.

Findings

Critical points occur at extremal black hole configurations.

Phase transitions from extremal to nonextremal states are identified.

Critical exponents satisfy scaling laws, linked to entropy homogeneity.

Abstract

We study the critical behavior in the black p-branes and four dimensional charged dilaton black holes. We calculate the thermodynamic fluctuations in the various (microcanonical, canonical, and grandcanonical) ensembles. It is found that the extremal limit of some black configurations has a critical point and a phase transition takes place from the extremal to nonextremal black configurations. Some critical exponents are obtained, which satisfy the scaling laws. This is related to the fact that the entropy of these black configurations is a homogeneous function.