Nonlinear Yang-Mills black holes

TL;DR

This paper introduces new classes of nonlinear Yang-Mills black hole solutions in various dimensions, analyzing their thermodynamic stability and phase transitions, revealing unique behaviors not seen in linear or other nonlinear models.

Contribution

It presents novel nonlinear Yang-Mills black hole solutions with detailed thermodynamic analysis, including stability and phase transition phenomena, in different spacetime dimensions.

Findings

Solutions can be naked singularities or black holes with multiple horizons.

Small charge solutions may be thermally stable in certain ensembles.

Reentrant phase transitions observed in BI-branch black holes with small eta.

Abstract

This paper is devoted to investigating the nonlinear non-abelian Yang-Mills black holes. We consider three Born-Infeld, exponential, and logarithmic nonlinear Yang-Mills theories with $SO(n-1)$ and $SO(n-2,1)$ semi-simple groups, which n is the dimension of spacetime, and obtain a new class of nonlinear Yang-Mills (NYM) black hole solutions. Depending on the values of dimension $n$, Yang-Mills charge $e$ and the mass $m$ and nonlinear parameters $\beta$, our solutions can lead to a naked singularity, a black hole with two horizons, an extreme or a Schwarzschild-type black hole. We also investigate the thermodynamic behaviors of the NYM black holes. For small charge values, the NYM solutions may be thermally stable in the canonical ensemble, if we consider an AdS spacetime with spherical $k=+1$ and hyperbolic $k=-1$ coordinates or a flat one with $k=+1$. However, there are no stable regions in the grand canonical ensemble in higher dimensions. For the NYM black hole, we observe a reentrant phase transition between large and small black holes in the BI-branch with small $\beta$, which cannot be visible for the nonlinear Reissner-Nordstrom AdS black hole in the higher dimension. For the limit $\beta\rightarrow\infty$, the critical ratio $\frac{P_{c} v_{c}}{T_{c}}$ tends to the constant value $3/8$ for each dimension $n$, while it depends on the dimension for the case of nonlinear electrodynamics black holes.