Photon sphere and phase transition of d-dimensional (d ≥ 5) charged Gauss-Bonnet AdS black holes

Shan-Zhong Han,Jie Jiang,Ming Zhang,Wen-Biao Liu

Figure 1. The effective potential ${V}_{\mathrm{eff}}(r)$ of a five-dimensional charged Gauss-Bonnet AdS black hole denoted by blue curve. The impact parameter of the photons moving in each region satisfies the following conditions respectively: I: $\chi \lt \sqrt{{V}_{\mathrm{eff}}(P)};$ II: $\chi \gt \sqrt{{V}_{\mathrm{eff}}(P)};$ III: $\chi \gt \sqrt{{V}_{\mathrm{eff}}(P)}$. For photons in region III, no matter they are ingoing or outgoing, they will all fall into the black hole in the end. Region IV denotes the potential barrier, region V denotes the interior of the black hole, yellow point P corresponds to photon sphere on which the photon has the maximum effective potential ${V}_{\mathrm{eff}}(P)$. Here, we set M = 1, Q = 0.02, α = 0.1, P = 0.05.