Thermodynamics of rotating thin shells in the BTZ spacetime

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 Bañados-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 ansätze 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.

17 pages

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• A Hamiltonian approach for the Thermodynamics of AdS black holes
• Entropy of extremal black holes: horizon limits through charged thin shells, a unified approach
• Unified approach to the entropy of an extremal rotating BTZ black hole: Thin shells and horizon limits
• Thermodynamics and entropy of self-gravitating matter shells and black holes in $d$ dimensions
• Thermodynamics of extremal rotating thin shells in an extremal BTZ spacetime and the extremal black hole entropy
• Compact objects in general relativity: From Buchdahl stars to quasiblack holes
• Effect of the self-gravity of shells on a high energy collision in a rotating Bañados-Teitelboim-Zanelli spacetime
• Thin shells associated to black string spacetimes
• Adiabatic analysis of the rotating BTZ black hole
• Black Holes Thermodynamics in a new kind of Noncommutative Geometry
• Thermodynamics of $d$-Dimensional Charged AdS (Anti-de Sitter) Black Holes: Hamiltonian Approach and Clapeyron Equation
• Thermodynamics of bosonic systems in adS spacetime
• Thermodynamic Stability of a Schwarzschild Thin-Shell Wormhole
• Generating Kerr-anti-de Sitter thermodynamics
• Studies on Thin-shells and Thin-shell Wormholes
• Thermodynamical and dynamical stability of Einstein-Maxwell and extremal Einstein-Born-Infeld thin shells in $(2+1)$ dimensions