The self-force on point particles in curved spacetime and quadrupole moments of rotating neutron stars

An expression for the self-force on a scalar point charge moving in a curved spacetime is calculated. This is done by first using a formal expression for the retarded Green function to compute the scalar field and the gradient of the scalar field in close proximity to the charge. (In the process, we correct a small error in Quinn's expression for the gradient.) Our method of computing the force closely parallels the method Dirac [1], and DeWitt and Brehme [2] used for finding the force on electric charges. We use our expression for the gradient of the field to find the flux flowing through a small tube surrounding the world-line of the particle. The momentum flow out of the tube is compensated by a change in momentum of the material particle inside the tube, thus giving us the force on the particle. We go to some length to present the calculation in a simple and pedagogical way showing many intermediate steps and using modern notation and conventions.;A rotating stars oblateness creates a deformation in the gravitational field outside the star, which is measured by the quadrupole-moment tensor. In a binary inspiral of rapidly rotating stars, the quadrupole moment (denoted by Q) of the stars dominates the departure from a point-particle waveform. It is known that induced quadrupole deformation causes the coalescence of binary inspiral to speed up and the deformation due to rotation can be expected to have a similar effect. Poisson [3] found that in the case of circular orbits, the quadrupole-monopole interaction affects the relation between orbital radius and angular velocity, and also the rate of inspiral.;Laarakkers and Poisson[4] have calculated quadrupole moments to high precision for rapidly rotating neutron stars. However their computation has an error in it arising from the fact the quadrupole moment is not an invariant quantity. We correct this error in the present work. We also construct a quadrupole moment maximizing equation of state and find an upper limit for quadrupole moment consistent with causality. Finally we formulate an empirical formula for computing the quadrupole moment of a rapidly rotating neutron star.