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.

中文翻译：

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d 维 (d ≥ 5) 带电 Gauss-Bonnet AdS 黑洞的光子球和相变

受最近工作的启发，光子球半径的非单调行为可用于反映 Reissner-Nordstr$\ddot{o}$m-AdS (RN-AdS) 黑洞的黑洞相变，我们研究了五维情况带电的 Gauss-Bonnet-AdS (GB-AdS) 黑洞在减少的参数空间中。我们发现光子球半径的非单调行为仍然存在。使用从 $PV$ 平面计算的共存线，我们捕获了饱和的小黑洞和大黑洞的光子球半径（共存阶段的边界），然后说明缩小的共存区域。结果表明，减少的共存区域随着电荷$Q$而减少，但随着Gauss-Bonnet系数$\alpha$而增加。当电荷消失时，减少的共存区域不再随高斯-博内系数$\alpha$而变化。在这种情况下，Gauss-Bonnet 系数 $\alpha$ 的作用与五维 RN-AdS 黑洞的电荷相同。并且，最后研究了更高维度的情况。