Entropy Evolution in the Interior Volume of a Charged f(R) Black Hole

Based on the 4-dimensional black hole solution of f(R) theory coupled to a nonlinear Maxwell field, we calculate the interior volume of a charged f(R) black hole using the method proposed by Christodoulou and Rovelli.Considering massless scalar field in the interior volume and Hawking radiation carrying only energy, we calculate the entropy of the scalar field inside a charged f(R) black hole and investigate the evolution of the entropy under Hawking radiation. In the meantime, the evolution of the Bekenstein-Hawking entropy under Hawking radiation has also been calculated. Based on these results, the proportional relation is obtained between the evolution of the scalar field entropy and the evolution of Bekenstein-Hawking entropy under Hawking radiation. According to the result, we investigate and discuss how the modified coefficient b in f(R) gravity theory affects the evolution relation between the two types of entropy. It is shown that the radiation rate for Hawking radiation of a charged f(R) black hole can increase with the modified coefficient b.