Determination of properties of cold stars in general relativity by a variational method

Approximate analytic formulae are obtained for the mass, the number of baryons, and the radius of a cold star by applying the energy variational principle in general relativity to a uniformdensity sphere of baryons. Conditions for equilibrium and for stability are expressed by transcendental equations which generalize familiar results of Newtonian theory. These formulae allow one to understand readily how various assumptions concerning the equation of state affect the properties of a neutron star. Comparison with some numerical calculations in the literature based on the differential equation for hydrostatic equilibrium in general relativity indicates that our analytic approximations are in reasonable quantitative agreement with exact results. By making use of the condition that the speed of sound is less than the speed of light, and of properties of neutron matter near nuclear densities, we derive an upper limit to the maximum mass of a stable neutron star. Subject headings: interiors, stellar - neutron stars - relativity