A new form of initial curvature scalar for calculating f(R) gravity

Previous literature applied the RVB method to various black holes\cite{12,13,14,15} under general relativity. Therefore, whether the RVB complex coordinate system makes it difficult to calculate the temperature of many memorable black holes, it is found that the Hawking temperature of black holes under f(R) gravity can be easily obtained by the RVB method. In one of the works of literature\cite{16}, an attempt was made to apply the RVB method to calculate the Hawking temperature of a black hole under f(R) gravity. When calculating the Hawking temperature, we found a difference in the constant of integration between the RVB and the general method. In an article\cite{19}, a hypothesis was proposed. The form of the new gravitational constant concerning the curvature scalar is deduced in it. This paper concludes a new scalar form of initial curvature under f(R) gravity by combining those two pieces of literature.