Statistical-mechanical entropy by the thin-layer method

Abstract

G. 't Hooft first studied the statistical-mechanical entropy of a scalar field in a Schwarzschild black hole background by the brick-wall: method and hinted that the statistical-mechanical entropy is the statistical origin of the Bekenstein-Hawking entropy of the black hole. However, according to our viewpoint, the statistical-mechanical entropy is only a quantum correction to the Bekenstein-Hawking entropy of the black hole. The brick-wall method based on thermal equilibrium at a large scale cannot be applied to the cases out of equilibrium such as a nonstationary black hole. The statistical-mechanical entropy of a scalar field in a nonstationary black hole background is calculated by the thin-layer method. The condition of local equilibrium near the horizon of the black hole is used as a working postulate and is maintained for a black hole which evaporates slowly enough and whose mass is far greater than the Planck mass: The statistical-mechanical entropy is also proportional to the area of the black hole horizon. The difference from the stationary black hole is that the result relies on a time-dependent cutoff.