A Note on Critical Nonlinearly Charged Black Holes

TL;DR

This paper explores the thermodynamics and particle dynamics of critical nonlinearly charged black holes, comparing power Yang-Mills and Maxwell systems, revealing conditions for efficiency convergence and dominance based on nonlinearity parameters.

Contribution

It provides a comparative analysis of power Yang-Mills and Maxwell black holes at criticality, highlighting how nonlinearity parameters influence thermodynamic efficiency and particle motion.

Findings

Efficiency approaches Carnot limit when parameters are equal to 1.

Maxwell system dominates for parameters less than 1, Yang-Mills for greater than 1.

Critical mass to charge ratio varies with the nonlinearity parameter.

Abstract

Within the extended phase space thermodynamics, we study aspects of power Yang-Mills and power Maxwell black holes at criticality, as the corresponding non-linearity power parameters $\gamma$ and $s$ are varied. On comparison, the approach of efficiency of heat engines to Carnot limit in both the systems is shown to coincide when $\gamma =s=1$. For $\gamma=s> (<) 1$, Maxwell (Yang-Mills) system dominates over Yang-Mills (Maxwell). The motion of charged particles in the critical Power Yang-Mills system is then investigated, together with a study of variation of critical mass to charge ratios with the power $\gamma$.