Homogeneous spheres with constant adriatic index

Compressible homogeneous spheres with constant adiabatic index γ were studied for their dynamical stability by Chandrasekhar and he found that for each value of u (≡ mass to size ratio), there is a value of γ = γ_c, such that for γ < γ_c, the configuration is dynamically unstable. On examining the properties of the Chandrasekhar's spheres (homogeneous spheres with constant γ) it is found that these spheres are non-isentropic, and the speed of sound within these spheres is finite. The authors find that (i) for the causality condition to be fulfilled throughout the configuration, the value of γ ≤ [2/(surface redshift)], (ii) for a given value of u, the binding coefficient, α_r = (M_r -M)/M, vanishes for some value of γ = γ_b and for all the values of γ < γ_b the configurations are unbound, and (iii) for u≤ (1/3), one can find configurations which are bound, dynamically stable, and the speed of sound is less than that of light throughout the configuration, whereas, for u >(1/3), the physically viable models of homogeneous density distribution are not possible. If the configuration is considered to be isentropic, then both γ and the speed of sound become infinite throughout the configuration. This revised version was published online in July 2006 with corrections to the Cover Date.