Timing Effects of Gravitational Waves from Localized Sources

Localized astronomical sources like a double stellar system, rotating neutron star, or a massive black hole at the center of the Milky Way emit periodic gravitational waves. For a long time only a far-zone contribution of gravitational fields of the localized sources (plane-wave-front approximation) were a matter of theoretical analysis. We demonstrate how this analysis can be extended to take into account near-zone and intermediate-zone contributions as well. The formalism is used to calculate gravitational-wave corrections to the Shapiro time delay in binary pulsars and low-frequency (LF) pulsar timing noise produced by an ensemble of double stars in our galaxy.