Gravitational two-body problem with arbitrary masses, spins, and quadrupole moments

Abstract

We find the precession of the spin and the precession of the orbit for the two-body problem in general relativity with arbitrary masses, spins, and quadrupole moments. One notable result which emerges is that, in the case of arbitrary masses ${m}_{1}$ and ${m}_{2}$, the spin-orbit contribution to the spin precession of body 1 is a factor $\frac{({m}_{2}+\frac{\ensuremath{\mu}}{3})}{({m}_{1}+{m}_{2})}$ times what it would be for a test body moving in the field of a fixed central mass (${m}_{1}+{m}_{2}$). Here $\ensuremath{\mu}$ denotes the reduced mass $\frac{{m}_{1}{m}_{2}}{({m}_{1}+{m}_{2})}$. This contrasts with the result of Robertson for the periastron precession where the corresponding factor is unity. These results may be of interest for binary neutron stars and, in particular, for binary pulsars such as PSR 1913+16.