Photon sphere and phase transition of ddimensional(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–Nordstr?m–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 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 coefficientα.When the charge vanishes,reduced coexistence region does not vary with Gauss–Bonnet coefficientαany more.In this case,the Gauss–Bonnet coefficientαplays the same role as the charge of five-dimensional RN–AdS black holes.Also,the situation of higher dimension is studied in the end.