Abstract
Abstract Recently, Hawking radiation of the black hole has been studied using the tunnel effect method. It is found that the radiation spectrum of the black hole is not a strictly pure thermal spectrum. How does the departure from pure thermal spectrum affect the entropy? This is a very interesting problem. In this Letter, we calculate the partition function by energy spectrum obtained from tunnel effect. Using the partition function, we compute the black hole entropy and derive the expression of the black hole entropy after considering the radiation. And we derive the entropy of charged black hole. In our calculation, we consider not only the correction to the black hole entropy due to fluctuation of energy but also the effect of the change of the black hole charges on entropy. There is no other hypothesis. Our result is more reasonable. According to the fact that the black hole entropy is not divergent, we obtain the lower limit of Banados–Teitelboim–Zanelli black hole energy. That is, the least energy of Banados–Teitelboim–Zanelli black hole, which satisfies the stationary condition in thermodynamics.
Highlights
Black holes have an event horizon from which any matter or information cannot escape
Each method means that taking the horizon area of the black hole as an entropy is self-consistent
When the horizon area of the black hole has been taken as entropy, the energy and temperature of the black hole satisfy thermodynamic law
Summary
Black holes have an event horizon from which any matter or information cannot escape. At present, discussing the entropy of black hole-matter coupling system becomes a meaningful problem This problem may provide a way for solving the difficulty of quantum gravitation. In recent years, string theory and Loop quantum gravity both had succeeded statistically in explaining the black hole entropy-area law [9,10]. In 1992 Banados, Teitelboim and Zanelli (BTZ) [23,24]showed that (2+1)-dimensional gravity has a black hole solution. This black hole is described by two (gravitational) parameters, the mass M and the angular momentum J It is locally AdS and it differs from the Schwarzschild and Kerr solutions since it is an asymptotically anti-de Sitter instead of a flat space-time. We calculate the partition function of BTZ black hole using the radiation spectrum obtained in tunnel process.
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