Fundamental thermodynamical equation of a self-gravitating system

Details Fundamental thermodynamical equation of a self-gravitating system Fundamental thermodynamical equation of a self-gravitating system

1996-01-23

arxiv.org/abs/gr-qc/9601037v2

Phys.Rev. D53 (1996) 7062-7072

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

30 pages, Revtex, no figures; Introduction rewritten and small changes included throughout to improve presentation; to appear

Scientific paper

10.1103/PhysRevD.53.7062

The features of the fundamental thermodynamical relation (expressing entropy as function of state variables) that arise from the self-gravitating character of a system are analyzed. The models studied include not only a spherically symmetric hot matter shell with constant particle number but also a black hole characterized by a general thermal equation of state. These examples illustrate the formal structure of thermodynamics developed by Callen as applied to a gravitational configuration as well as the phenomenological manner in which Einstein equations largely determine the thermodynamical equations of state. We consider in detail the thermodynamics and quasi-static collapse of a self-gravitating shell. This includes a discussion of intrinsic stability for a one-parameter family of thermal equations of state and the interpretation of the Bekenstein bound. The entropy growth associated with a collapsing sequence of equilibrium states of a shell is computed under different boundary conditions in the quasi-static approximation and compared with black hole entropy. Although explicit expressions involve empirical coefficients, these are constrained by physical conditions of thermodynamical origin. The absence of a Gibbs-Duhem relation and the associated scaling laws for self-gravitating matter systems are presented.

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