Rotating neutron stars in general relativity - Exact solutions for the case of slow rotation

Abstract

Two new solutions to Einstein's field equations are presented which are valid for the case of slow rotation. These new solutions represent uniformly rotating spheres which may be of use as neutron star and pulsar models. One solution is a family of fluid spheres which have vanishing pressure at the surface. It is not necessary to introduce a discontinuous region over which the pressure is brought to zero as is the case with solutions based on the polytropic equation of state of Misner and Zapolsky. The second solutions depicts a uniformly rotatin sphere composed of solid matter of constant density. This solution represents the most compact mass undergoing slow rotation possible within the framework of general relativity. Any pulsar safisfying the conditions of slow rotation and requiring parameters based on a more compact object must of necessity be a black hole. The matching of these solutions to form neutron stars with both solid and fluid components is considered.