Steepest descent technique and stellar equilibrium statistical mechanics. V Relativistic systems with an energy cutoff

Physics – Condensed Matter – Statistical Mechanics

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Astrodynamics, Relativity, Star Clusters, Statistical Mechanics, Red Shift, Steepest Descent Method, Systems Stability, Thermodynamic Properties

Scientific paper

Relativistic star clusters with an energy cutoff, at fixed energy and number of particles, are thermodynamically unstable for central redshifts greater than 0.55; this agrees with previous estimates based on dynamical perturbation calculation. Our conclusions are derived from statistical mechanics analysis, giving necessary and sufficient conditions of stability of mean field configurations. Criteria of stability are independent of how relativistic the system may be. It is proved that isolated clusters become unstable when the heat capacity becomes equal to zero. It is also shown that the binding energy, as a function of the redshift at the center, passes through a minimum at the onset of instability.

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