The stability of relativistic gas spheres⋆
E. N. GlassPhysics Department, University of Windsor, Windsor, Ontario N9B 3P4, CanadaAmos HarpazPhysics Department, University of Windsor, Windsor, Ontario N9B 3P4, Canada
1983en
ABI
Abstract
The eigenvalue problem for linear adiabatic radial perturbations of relativistic gas spheres is presented in a tridiagonal matrix formulation. Two classes of relativistic polytropes are studied. Curves of marginal stability are found in the (n, q) parameter plane, where n is the poly tropic index and q is the ratio of central pressure to density. Jeans' criterion for relativistic gas spheres is established and a local, purely general relativistic, instability is exposed. It is also shown that the sign of the binding energy is unrelated to stability against small perturbations.
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