Study on the RVB method for calculating the Hawking temperature of black holes

In this work, we study the RVB method for calculating the Hawking temperature of different black holes and find that there is an undetermined integral constant in the temperature expression. We use this method to calculate the Hawking temperature of the black hole in Einstein gravity, and massive gravity, Einstein–Gauss–Bonnet gravity, Scalar–Tensor–Vector modified gravity and f(R) gravity, respectively. By comparing with the temperature obtained by the Hawking temperature formula, we find that regardless of the gravitational theory from which the black hole solution is obtained, after the black hole metric is reduced to two dimensions, if there is no first-order term of r in g00, the integral constant is 0. If there is a first-order term of r in g00, the integral constant is determined by the coefficient in front of the first-order term of r.