Rivelazione di onde gravitazionali attraverso l'Astrometria relativistica

The aim of this work is to assess the observability of the variations in angular separations of pairs of close stars induced in the observer spacetime by passing gravitational waves. The study of the prospects for detecting gravitational waves is based on method of relativistic astrometry in space. After an introduction on gravitational waves and methods used to detect them, we briefly address previous studies on the detection of light deflection induced by gravitational waves using high precision astrometry. Then, we describe a novel formulation of the astrometric observable, that is the cosine of the angle between the lines of sight to two close distant point-like (stars or quasars) sources, calculated at the observer in the Solar System’s geometry perturbed by passing gravitational waves. From this result, the astrometric gravitational antenna can be devised as a telescope in space pointing simultaneously at three mutually orthogonal lines of sight. Using this operating principle, it is possible to determine the amplitude and frequency of a wave, and pinpoint the direction to the gravitational source with precision sub-arcsecond. We implement the derived formulas in the case of gravitational waves produced by periodic binary systems to estimate the corresponding angular perturbations; these results highlight the potential of the astrometric antenna to explore frequency ranges still not covered by current and future ground- based and space-borne gravitational waves detection programs. Finally, we estimate the angular variations induced by coalescing compact binaries to show complementarity with the linear antennas like the LIGO-Virgo collaboration.