Entropy extremum of relativistic self-bound systems: A geometric approach

Journal Article · Fri Aug 15 00:00:00 EDT 1975 · Phys. Rev., D, v. 12, no. 4, pp. 956-964

DOI:https://doi.org/10.1103/PhysRevD.12.956· OSTI ID:4179433

Katz, J; Manor, Y

Conditions for entropy extremum of self-bound relativistic systems of particles, in stationary axisymmetric motion, are obtained under the following constraints: (i) The system is kept isolated in a geometrical sense, implying that the total mass--energy and total angular momentum, defined by the asymptotic behavior of the metric, are kept constant, (ii) the total number of particles is kept constant, and (iii) Einstein's constraint equations are imposed on a spacelike hypersurface. It is shown that if the system is in mechanical equilibrium, the total entropy is an extremum for all trial nonequilibrium configurations that satisfy the constraints and respect the symmetry, if and only if (i) Einstein's dynamical equations are satisfied, (ii) the temperature and the gravito-chemical potential, as seen from infinity, are constant, and (iii) the system is rigidly rotating. The proof does not depend on a particular functional expression for the mass of for the angular momentum; consequently, no related Lagrange multipliers have been used.

• Research Organization: The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel
• Sponsoring Organization: USDOE
• NSA Number: NSA-33-003740
• OSTI ID: 4179433
• Journal Information: Phys. Rev., D, v. 12, no. 4, pp. 956-964, Other Information: Orig. Receipt Date: 30-JUN-76
• Country of Publication: United States
• Language: English

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METRICS
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