The canonical ensemble of a self-gravitating matter thin shell in AdS

Abstract

We build the canonical ensemble of a hot self-gravitating matter thin shell in anti-de Sitter (AdS) space by finding its partition function through the Euclidean path integral approach with fixed temperature at the conformal boundary. We obtain the reduced action of the system by restricting the path integral to spherically symmetric metrics with given boundary conditions and with the Hamiltonian constraint satisfied. The stationary conditions, i.e., the mechanical equilibrium and the thermodynamic equilibrium, are obtained from minimizing the reduced action. Evaluating the perturbed reduced action at the stationary points yields the mechanical stability condition and the thermodynamic stability condition. The reduced action calculated at the stationary points gives the partition function in the zero-loop approximation and from it the thermodynamic properties of the system are acquired. Within thermodynamics alone, the only stability condition that one can establish is thermodynamic stability, which follows from the computation of the heat capacity. For given specific pressure and temperature equations of state for the shell, we obtain the solutions of the ensemble. There are four different thin shell solutions, one of them is fully stable, i.e., is stable mechanically and thermodynamically. For the equations of state given, we find a first order phase transition from the matter thermodynamic phase to the Hawking-Page black hole phase. Moreover, there is a maximum temperature above which the shell ceases to exist, presumably at these high temperatures the shell inevitably collapses to a black hole.

31 pages, 9 figures, typos corrected

References in corpus (16)

• Thermodynamics of Reissner-Nordstrom-anti-de Sitter black holes in the grand canonical ensemble
• Fundamental thermodynamical equation of a self-gravitating system
• Thermodynamics of toroidal black holes
• Thermodynamics of the two-dimensional black hole in the Teitelboim-Jackiw theory
• Phase transitions and critical behavior of black branes in canonical ensemble
• Entropy of quasiblack holes
• Thermodynamics of five-dimensional Schwarzschild black holes in the canonical ensemble
• Entropy of extremal black holes from entropy of quasiblack holes
• Thermodynamics of $d$-dimensional Schwarzschild black holes in the canonical ensemble
• Entropy of a self-gravitating electrically charged thin shell and the black hole limit
• Grand canonical ensemble of a $d$-dimensional Reissner-Nordström black hole in a cavity
• Schwarzschild-anti de Sitter within an Isothermal Cavity: Thermodynamics, Phase Transitions and the Dirichlet Problem
• 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
• Electrically charged spherical matter shells in higher dimensions: Entropy, thermodynamic stability, and the black hole limit
• Gibbons-Hawking action for electrically charged black holes in the canonical ensemble and Davies' thermodynamic theory of black holes