Black hole entropy and models
No universally accepted statistical explanation of black hole entropy exists up to now, therefore, it is worth another try. Admittedly, black hole entropy does not have to have a statistical origin. If the "black hole entropy" is called "black hole index" instead, someone might be lured to give it an economic explanation. Nonetheless, the only way to justify one's claim about the statistical origin of black hole entropy is to compute it statistically. This is the motivation for the construction of black hole models. In chapter 1, I first review the four laws of classical black hole mechanics which form the basis for the introduction of black hole thermodynamics. After observing the formal analogy between the four laws of the black hole mechanics and that of the ordinary thermodynamics, I further explore the thermodynamic properties of black holes in chapter 2 by reviewing the phenomenon of Hawking radiation and introducing the idea of black hole entropy. Three statistical explanations of black hole entropy are introduced in chapter 3. I will start with’t Hooft's brick wall model. Then, á la Brown and York, I review the approach based on the gravitational degrees of freedom via path integral. In the final part of this chapter, I present my own version of a quantum statistical explanation of black hole entropy by regarding a black hole as a cavity with thermal states inside. The final chapter will be devoted to the construction of black hole models to materialise the idea that a black hole, in some sense, can be regarded as a cavity where thermalised quantum states reside with quantised spectrum. These quantum states and the corresponding spectrum will then justify the statistical explanation of black hole entropy presented in the final section of chapter 3.