Photon orbits and thermodynamic phase transition of $d$-dimensional charged AdS black holes

TL;DR

This paper investigates how photon orbits relate to thermodynamic phase transitions in charged AdS black holes across various dimensions, revealing universal critical behavior and potential order parameters.

Contribution

It uncovers the non-monotonic behavior of photon sphere radius and impact parameter as indicators of black hole phase transitions, demonstrating universality across dimensions.

Findings

Photon sphere radius and impact parameter show non-monotonic behavior below critical pressure.

These quantities can serve as order parameters for small-large black hole transitions.

Universal critical exponent of 1/2 near the critical point across dimensions.

Abstract

We study the relationship between the null geodesics and thermodynamic phase transition for the charged AdS black hole. In the reduced parameter space, we find that there exist non-monotonic behaviors of the photon sphere radius and the minimum impact parameter for the pressure below its critical value. The study also shows that the changes of the photon sphere radius and the minimum impact parameter can serve as order parameters for the small-large black hole phase transition. In particular, these changes have an universal exponent of $\frac{1}{2}$ near the critical point for any dimension $d$ of spacetime. These results imply that there may exist universal critical behavior of gravity near the thermodynamic critical point of the black hole system.