Entropy of eternal black holes

TL;DR

This paper investigates the entropy of eternal black holes using a microcanonical functional integral approach, revealing that the entropy is zero in the semiclassical approximation and highlighting the pure state nature of the system.

Contribution

It introduces a method to include internal degrees of freedom of black holes in path integral thermodynamics, providing new insights into black hole entropy calculations.

Findings

Entropy equals zero in the semiclassical approximation.

Functional integral reflects a pure state.

Internal degrees of freedom can be explicitly included.

Abstract

The entropy of a quantum-statistical system which is classically approximated by a general stationary eternal black hole is studied by means of a microcanonical functional integral. This approach opens the possibility of including explicitly the internal degrees of freedom of a physical black hole in path integral descriptions of its thermodynamical properties. If the functional integral is interpreted as the density of states of the system, the corresponding entropy equals ${cal S} = A_H/4 - A_H/4 =0$ in the semiclassical approximation, where $A_H$ is the area of the black hole horizon. The functional integral reflects the properties of a pure state.