Non-rigid massive spheres in general relativity

Abstract

Solutions corresponding to spheres with a slowly varying density <f>$(\\rho\\propto1-r^2/K^2)$</f> are evaluated. This has been applied to construct a model of a neutron star. The mass of a neutron star comes out to be 3.34 <it>M</it><inf>⊙</inf>, when everywhere the speed of sound remains less than the speed of light. Under extreme conditions the mass of a neutron star approaches the limit of 8 <it>M</it><inf>⊙</inf>. The mass/radius ratio for the physical condition <f>$P=(1/3)\\rho$</f> comes out to be more than that for a constant density sphere.