An Exact Study of Rigidly and Rapidly Rotating Stars in General Relativity with Application to the Crab Pulsar

A previous method of numerical integration of the Einstein equations is applied to the problem of equilibrium configurations of relativistic rigidly rotating stars. The treatment is made with no approximations. Two cases are considered: the relativistic noninteracting Fermi gas and the incompressible fluid. The case of the Fermi gas is applied to neutron stars. Baryonic number, gravitational mass, and binding energy of a neutron star are given as functions of central density and angular velocity. The usual expression (EL = 21I* 2), where EL is the energy stored by rotation, the angular velocity, and 1* the inertial momentum, is shown to hold to a good approximation. A formula involving I and the baryonic number is also given. The inner isobaric surfaces are found to be prolate. As a consequence, and if the core of a star is in a solid state, negative glitches may occur. The incompressible-fltiid case is studied in both Newtonian and relativistic conditions. A check of our method is furnished by a comparison of the classical analytical calculation and the Newtonian limit. In medium-relativistic conditions, we find the same correction to angular velocity as in the post-Newtonian approximation, but in more relativistic conditions our correction becomes larger. For larger central pressures (relativistic conditions), the post-Newtonian result for the redshift at pole of the star is found anew. In intermediate cases, the same corrections to angular velocity as in the post-Newtonian approximation are also found, although for larger central pressure these corrections are slightly larger. Subject headings: neutron stars - pulsars - rotation, stellar