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

Abstract

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.

Correction to Black Hole Entropy Variation under Hawking Radiation

“…(2) shows that increasing or decreasing the emissivity factor lead to greatly affects on the emission of radiation from black hole. This result generalizes our earlier study of black hole evaporation [11,12]. In comparison to this result, our earlier investigations for black hole as black body can be considered as a special case of this study.…”

“…Using two assumptions, an evolution relation is obtained between the interior and exterior entropy and important discussion is contributed to the literature of black hole physics for detail also see Refs. [10,11,12]. Here are some points, which need attention to make some advancement in above discussion.…”

Resolving the Information Paradox with Probabilistic Spacetime

“…That analysis was quickly challenged conceptually in two ways: 1) the "failure" to define the paradox in terms of entanglement and 2) the lack of mechanism for how the correlations allow for information recovery [18], with a rebuttal from the original researchers [19]. Subsequent researchers have typically expressed the correlational correction represents progress but have not seen it as sufficiently complete to resolve the paradox due to its lack of mechanism [20] [21] [22] [23].…”

Entropy variation of rotating BTZ black hole under Hawking radiation

“…The investigation of a relation between the interior and exterior entropy of black hole could led to discuss the black hole evaporation [2]. So, using the notion of interior entropy with two important assumptions of 'black hole radiations as black body radiations' and 'the emission rate as quasi-static' it was found that the rate of change of interior entropy is related to the Bekenstein-Hawking entropy by a simple relation as discussed in [14,16,22].…”