# Photon sphere and phase transition of $d$-dimensional ($d\ge5$) charged Gauss-Bonnet AdS black holes

## TL;DR

This paper investigates how photon sphere radius behaviors relate to phase transitions in five-dimensional charged Gauss-Bonnet-AdS black holes, revealing nonmonotonic patterns and the influence of charge and Gauss-Bonnet coefficient on coexistence regions.

## Contribution

It extends the study of photon sphere behaviors to higher-dimensional Gauss-Bonnet-AdS black holes, analyzing phase transition indicators and the effects of charge and Gauss-Bonnet coupling.

## Key findings

- Photon sphere radius exhibits nonmonotonic behavior during phase transitions.
- Reduced coexistence region decreases with charge but increases with Gauss-Bonnet coefficient.
- When charge is zero, the Gauss-Bonnet coefficient acts like the black hole charge.

## Abstract

Motivated by recent work, nonmonotonic behaviours of photon sphere radius can be used to reflect black hole phase transition for Reissner-Nordstr$\ddot{o}$m-AdS (RN-AdS) black holes, we study the case of five-dimensional charged Gauss-Bonnet-AdS (GB-AdS) black holes in the reduced parameter space. We find that the nonmonotonic behaviours of photon sphere radius still exist. Using the coexistence line calculated from $P-V$ plane, we capture the photon sphere radius of saturated small and large black holes (the boundary of the coexistence phase), then illustrate the reduced coexistence region. The results show that, reduced coexistence region decreases with charge $Q$ but increases with Gauss-Bonnet coefficient $\alpha$. When the charge vanishes, reduced coexistence region doesn't vary with Gauss-Bonnet coefficient $\alpha$ any more. In this case, the Gauss-Bonnet coefficient $\alpha$ plays the same role as the charge of five-dimensional RN-AdS black holes. Also, the situation of higher dimension is studied in the end.