Photon orbits and phase transition for Non-Linear charged Anti-de Sitter black holes

TL;DR

This paper explores the connection between photon orbits and phase transitions in non-linear charged AdS black holes, revealing universal behaviors and critical exponents similar to thermal systems.

Contribution

It uncovers the relationship between photon sphere properties and phase transitions, introducing the impact parameter as an order parameter with universal critical exponents.

Findings

Photon sphere radius and impact parameter exhibit non-monotonic behavior near phase transitions.

Changes in photon sphere radius and impact parameter serve as order parameters with critical exponent 1/2.

Impact parameter influences the deflection angle of photons around black holes.

Abstract

In this work, we investigate the relationship between the photon sphere radius and the first-order phase transition for the charged EPYM AdS black hole. Through the analysis, we find with a certain condition there exist the non-monotonic behaviors between the photon sphere radius, the impact parameter, the non-linear YM charge parameter, temperature, and pressure. And both the changes of photon sphere radius and impact parameter before and after phase transition can be regarded as the order parameter, their critical exponents near the critical point are equal to the same value $1/2$, just like the ordinary thermal systems. These indicate that there maybe exists a universal relationship of gravity nearby the critical point for a black hole thermodynamical system. Furthermore, the effect of impact parameter on the deflect angle is also investigated.