Gauss-bonnet Gravity Of The Black Hole Quasi Regular Mode And Phase Change,

We have studied the scalar perturbation around the Ricci flat black hole and AdS soliton in Gauss-Bonnet gravity. First, we reviewed the phase transition between the Ricci flat black hole and AdS soliton and the scalar perturbation around these two background space-times in four-dimension Einstein's gravity. Second, we discussed the phase transition between these two background space-times by thermo-dynamical analysis. Then, we gave out the perturbation equations under the space-times of Ricci flat black hole as well as AdS soliton in five-dimension Gauss-Bonnet gravity. We used approximations to conquer the difficulties in calculation and show the rationality of our approximations.From the perturbation around the background space-times in the Gauss-Bonnet gravity, we find the physical evidence that Ricci flat AdS black holes and AdS solitons are different physical configurations and staying in different phases, this serves as a strong support to the previous mathematical and thermo-dynamical arguments.