Entropy of thin shells in a (2+1)-dimensional asymptotically AdS spacetime and the BTZ black hole limit

Abstract

The thermodynamic equilibrium states of a static thin ring shell in a (2+1)-dimensional spacetime with a negative cosmological constant are analyzed. Inside the ring, the spacetime is pure anti-de Sitter (AdS), whereas outside it is a Bañados-Teitelbom-Zanell$ (BTZ) spacetime and thus asymptotically AdS. The first law of thermodynamics applied to the thin shell, plus one equation of state for the shell's pressure and another for its temperature, leads to a shell's entropy, which is a function of its gravitational radius alone. A simple example for this gravitational entropy, namely, a power law in the gravitational radius, is given. The equations of thermodynamic stability are analyzed, resulting in certain allowed regions for the parameters entering the problem. When the Hawking temperature is set on the shell and the shell is pushed up to its own gravitational radius, there is a finite quantum backreaction that does not destroy the shell. One then finds that the entropy of the shell at the shell's gravitational radius is given by the Bekenstein-Hawking entropy.

arXiv comment9 pages

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• Entropy of a self-gravitating electrically charged thin shell and the black hole limit
• Spherical and nonspherical models of primordial black hole formation: exact solutions
• Geodesically complete BTZ-type solutions of $2+1$ Born-Infeld gravity
• Simulation of geodesic trajectory of charged BTZ black holes in massive gravity
• 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
• Compact objects in general relativity: From Buchdahl stars to quasiblack holes
• 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
• Thin shells associated to black string spacetimes
• Rotating thin shells in (2+1)-dimensional asymptotically AdS spacetimes: Mechanical properties, Machian effects, and energy conditions
• Adiabatic analysis of the rotating BTZ black hole
• C-metric in a (nut)shell
• Thermodynamical and dynamical stability of Einstein-Maxwell and extremal Einstein-Born-Infeld thin shells in $(2+1)$ dimensions
• Classical and Quantum Thermodynamic Systems in Curved Spacetime