A passing gravitational wave causes a deflection in the apparent astrometric positions of distant stars. The effect of the speed of the gravitational wave on this astrometric shift is discussed. A stochastic background of gravitational waves would re
sult in a pattern of astrometric deflections which are correlated on large angular scales. These correlations are quantified and investigated for backgrounds of gravitational waves with sub- and super-luminal group velocities. The statistical properties of the correlations are depicted in two equivalent and related ways: as correlation curves and as angular power spectra. Sub-(super-)luminal gravitational wave backgrounds have the effect of enhancing (suppressing) the power in low-order angular modes. Analytical representations of the redshift-redshift and redshift-astrometry correlations are also derived. The potential for using this effect for constraining the speed of gravity is discussed.
Extreme mass ratio in-spirals (EMRIs) are candidate events for gravitational wave detection in the millihertz range (by detectors like LISA and eLISA). These events involve a stellar-mass black hole, or a similar compact object, descending in the gra
vitational field of a supermassive black hole, eventually merging with it. Properties of the in-spiralling trajectory away from resonance are well known and have been studied extensively, however little is known about the behaviour of these binary systems at resonance, when the radial and lateral frequencies of the orbit become commensurate. We describe the two existing models, the instantaneous frequency approach used by Gair, Bender, and Yunes, and the standard two timescales approach implemented by Flanagan and Hinderer. In both cases, the exact treatment depends on the modelling of the gravitational self-force, which is currently not available. We extend the results in Gair, Bender and Yunes to higher order in the on-resonance flux modification, and argue that the instantaneous frequency approach is also a valid treatment of the resonance problem. The non-linear differential equations which arise in treating resonances are interesting from a mathematical view point. We present our algorithm for perturbative solutions and the results to third order in the infinitesimal parameter, and discuss the scope of this approach.
