Tunneling radiation as new perspective of understanding the thermodynamics in f ( R ) $f(R)$ gravity

Abstract

We use the Parikh-Wilczek method to study the tunneling radiation from the event horizon of a charged AdS black hole in \(f(R)\) gravity. The emission rate of a particle is calculated. The emission spectrum deviates from the pure thermal spectrum but consists with an underlying unitary theory. The emission rate of massive particles takes the same functional form as that of massless particles. Contradictory but interesting phenomenon is discovered. The expression of the emission rate for a black hole in \(f(R)\) gravity differs from that for a black hole in Einstein gravity, if the area-law of the black hole entropy is insisted on. Conversely, based on abandoning the area-law and admitting the conventional tunneling rate, we obtain the expressions of the entropy and the first law of thermodynamics for the \(f(R)\) gravity black hole, which is in accordance with the early results. So the research of tunneling radiation in this paper may serve as a new perspective of understanding the thermodynamics of black holes in \(f(R)\) gravity.