Thermodynamics of rotating thin shells in the BTZ spacetime

TL;DR

This paper studies the thermodynamic properties of a rotating thin shell in a (2+1)-dimensional anti-de Sitter spacetime, deriving its entropy and stability conditions, and connecting it to black hole thermodynamics.

Contribution

It derives the entropy of a rotating thin shell in BTZ spacetime from thermodynamic principles and relates it to black hole entropy, including stability analysis.

Findings

Shell entropy depends only on gravitational radii.

When shell temperature equals Hawking temperature, entropy matches Bekenstein-Hawking entropy.

Analytical stability conditions are obtained for specific equations of state.

Abstract

We investigate the thermodynamic equilibrium states of a rotating thin shell, i.e., a ring, in a (2+1)-dimensional spacetime with a negative cosmological constant. The inner and outer regions with respect to the shell are given by the vacuum anti-de Sitter and the rotating Ba\~{n}ados-Teitelbom-Zanelli spacetimes, respectively. The first law of thermodynamics on the thin shell, together with three equations of state for the pressure, the local inverse temperature and the thermodynamic angular velocity of the shell, yields the entropy of the shell, which is shown to depend only on its gravitational radii. When the shell is pushed to its own gravitational radius and its temperature is taken to be the Hawking temperature of the corresponding black hole, the entropy of the shell coincides with the Bekenstein-Hawking entropy. In addition, we consider simple ans\"atze for the equations of state, as well as a power-law equation of state where the entropy and the thermodynamic stability conditions can be examined analytically.