A shell of Bosons in Spherically Symmetric spacetimes

TL;DR

This paper investigates the thermodynamics of a bosonic shell near black hole horizons, revealing Bose-Einstein condensation at finite temperature and entropy behavior akin to black hole entropy, with extensions to higher dimensions.

Contribution

It introduces a covariant partition function for bosons in curved spacetime and analyzes their thermodynamic properties near black hole horizons, including entropy and condensation phenomena.

Findings

Bose-Einstein condensation occurs at non-zero temperature in curved spacetime.

Photon gas entropy near the horizon shows area dependence similar to Bekenstein-Hawking entropy.

Results extended to higher-dimensional spherically symmetric spacetimes.

Abstract

The thermodynamic properties of a shell of bosons with the inner surface locating at Planck length away from the horizon of Schwarzschild black holes by using statistical mechanics are studied. The covariant partition function of bosons is obtained, from which the Bose-Einstein condensation of bosons is found at a non-zero temperature in the curved spacetimes. As a special case of bosons, we analyze the entropy of photon gas near the horizon of the Schwarzschild black hole, which shows an area dependence similar to the Bekenstein-Hawking entropy. The results may offer new perspectives on the study of black hole thermodynamics. All these are extended to the $D+1$ dimensional spherically symmetric static spacetimes.