Post-Newtonian Jeans analysis

Abstract

The Jeans analysis is studied in the first post-Newtonian limit. In other words, the relativistic effects on the local gravitational instability are considered for systems where characteristic velocity of the system and corresponding gravitational field are higher than what permitted in Newtonian limit. The dispersion relation for propagation of small perturbations is found in the post-Newtonian approximation using two different techniques. A new Jeans mass is derived and compared to the standard Jeans mass. In this limit, the relativistic effects make the new Jeans mass to be smaller than the Newtonian Jeans mass. Furthermore, the fractional difference between these two masses increases when temperature/pressure of the system increases. Interestingly, in this limit pressure can help the gravitational instability instead of preventing it. Finally the results are applied to high temperature astrophysical systems and the possibility of local fragmentations in some relativistic systems is investigated.

14 pages, 5 figures, accepted for publication in ApJ

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• Post-Newtonian corrections to Toomre's criterion
• Plane wave analysis of the second post-Newtonian hydrodynamic equations
• Post-Newtonian Jeans Equation for Stationary and Spherically Symmetrical Self-Gravitating System
• Relaxation-Time Model for the Post-Newtonian Boltzmann Equation
• Stellar structure model in the post-Newtonian approximation
• Virial theorem for a cloud of stars obtained from Jeans equations with the second correlation moments
• Jeans Instability from post-Newtonian Boltzmann equation