Polytropic spheres with isothermal cores

The paper deals with massive fluid spheres with an isothermal core (having finite central density) and a polytropic envelope in terms of the General Relativity. The matching of the solutions in the core and envelope has been done using Bondi's condition,H=0 and also without it. The study reveals that since this condition does not correspond to any particular physical situation the maximum values of fractional core size, fractional core mass and the redshift do not occur atH=0, but that they occur at some other point. Within the permissible physical conditions (dP/dρ≤1) the maximum values ofM _core/M,R _core/R and the surface redshift, for an isothermal coreP=ρ/3, are respectively 0.473, 0.554, and 0.565. Using the conditionH=0, it has been shown that for isothermal cores corresponding to the equation of the stateP≥0.6ρ, the configurations are pulsationally unstable.