Photon orbits and phase transition for non-linear charged anti-de Sitter black holes

Abstract

In this work, we investigate the relation between the photon sphere radius and the first-order phase transition for the charged Einstein-power-Yang-Mills 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 Yang-Mills 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 relation 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.

Restricted Phase Space Thermodynamics of Einstein-Power-Yang–Mills AdS Black Hole

“…[ 38 ] and the corresponding optical properties including the photon sphere and shadow were also presented in Refs. [ 44 , 45 ]. Next, we will exhibit the concrete details of the restricted phase space formulism for the EPYM AdS black hole in the case of .…”

“…Based on the classification of phase transition for a thermodynamic system by Ehrenfest, the critical point can be obtained by the following equations With Equations ( 12 ) and ( 14 ) and the above equations, we have The other critical quantities in the restricted phase space are The results indicate that the critical point is determined by the non-linear YM parameter and the YM charge . Since the effect of on the phase transition has been investigated in previous works [ 38 , 44 ], here we only exhibit the effects of on the critical temperature, the critical pressure, and the critical central charge in Figure 1 . In the range , the critical temperature and pressure are both decreasing with the increase of , while the critical central charge is increasing.…”

“…In previous works [ 38 , 44 ], the phase transition condition of the EPYM AdS black hole in the extended phase space was proposed. Furthermore, the first-order phase diagrams of , , and in the extended phase space were also exhibited.…”