Microscopic derivation of the Bekenstein-Hawking entropy for Schwarzschild black holes

In this paper, we successfully derive the Bekenstein-Hawking entropy for Schwarzschild black holes in various dimensions by using a non-trivial phase space. It is appealing to notice that the thermodynamics of a Schwarzschild black hole actually behaves like that of a $1$-dimensional quantum mechanical system. Our result suggests that black hole should be viewed as a system with the equation of state $P=\rho$, and it also suggests that a holographic stage should exist in the early universe.