A bindingenergy criterion for the dynamical stability of spherical stellar systems in general relativity
Abstract
A sufficient condition for the dynamical stability of spherical stellar systems to collisionless spherical perturbations is derived within the framework of general relativity, by first solving the problem of determining which relativistic spherical systems locally maximize the value of the phasespace integral of a chosen function of the phase density. It is proven that a relativistic spherical stellar system in collisionless equilibrium is dynamically stable to collisionless perturbations if it maximizes the unique functional which it extremizes, implying that members of appropriate equilibrium sequences are stable at least up to the first maximum of the binding energy. The sufficient condition has been found to break down at a point which coincides, to within available numerical accuracy, with the calculated point of onset of dynamical instability.
 Publication:

The Astrophysical Journal
 Pub Date:
 June 1980
 DOI:
 10.1086/158076
 Bibcode:
 1980ApJ...238.1101I
 Keywords:

 Astrodynamics;
 Binding;
 Dynamic Stability;
 Relativity;
 Stellar Motions;
 Stellar Systems;
 Systems Stability;
 Boltzmann Transport Equation;
 Distribution Functions;
 Einstein Equations;
 Functionals;
 Perturbation Theory;
 Astrophysics