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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Glass et al. (1983) studied this question.