The origin of the area law of the entropy of a quantum field in a black hole

TL;DR

This paper demonstrates that the area law for the entropy of a quantum field in a Schwarzschild black hole arises primarily from quantum statistical effects, as shown through various statistical models and calculation methods.

Contribution

It reveals that the area law is due to quantum statistics, providing a unified explanation across different quantum gases and fields in black hole environments.

Findings

The area law holds when quantum statistical effects dominate.

Entropy calculations for different gases show consistent area dependence.

Quantum statistics are crucial for the entropy-area relationship in black holes.

Abstract

It is shown that that the area law for the entropy of a quantum field in the Schwarzschild black hole is due to the quantum statistics. The entropies for one particle, a Boltzmann gas, a quantum mechanical gas obeying Bose-Einstein or Fermi-Dirac statistics, and a quantum field in the Schwarzschild black hole are calculated using the microcanonical ensemble approach and the brick wall method. The area law holds only when the effect of quantum statistics is dominated.