Gravitational Radiation from Slowly Rotating, Fully Relativistic Stars

If pulsars are rotating neutron stars, they might be losing significant amounts of rotational energy by the emission of gravitational radiation. In this connection, it is important to know the rate at which a fully retatiZiStic rigidly rotating star emits gravitational radiation. In this paper, recently developed techniques are used to compute that rate for a relativistic star whose equatorial velocity of rotation is small compared with the velocity of light, and whose deformation from spherical symmetry is small. The deformation is supported by stresses which are anisotropic in general. The analysis yields an emission rate wbich is identical to tbat of standard weak-field theory, provided the multipole moments used in the weak-fidd formula are those which describe the star's Newtonian potential in the near-zone far-field region (gravitational radius r <K "velocity-of4ight circle"). The multipole moments are determined in terms of integrals involving the fully relativistic star's deformation. Also studied are the radiationreaction forces, whose presence inside the star accompanies the emission of radiation. These forces extract energy and angular momentum from the star at the same rates as the gravitational waves carry them away.