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

Motivated by recent work, nonmonotonic behaviors of photon sphere radius can be used to reflect black hole phase transition for Reissner-Nordstrom-AdS (RN-AdS) black holes, we study the case of five-dimensional charged Gauss-Bonnet-AdS black holes in the reduced parameter space. We find that the nonmonotonic behaviors of photon sphere radius still exist. Using the coexistence line calculated fromP-Vplane, 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 chargeQbut increases with Gauss-Bonnet coefficient alpha. When the charge vanishes, reduced coexistence region does not 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.