Relativistic analysis of the LISA long range optical links

The joint ESA/NASA LISA mission consists in three spacecraft on heliocentric orbits, flying in a triangular formation of 5 Mkm each side, linked by infrared optical beams. The aim of the mission is to detect gravitational waves in a low frequency band. For properly processing the scientific data, the propagation delays between spacecraft must be accurately known. We thus analyse the propagation of light between spacecraft in order to systematically derive the relativistic effects due to the static curvature of the Schwarzschild space-time in which the spacecraft are orbiting with time-varying light-distances. In particular, our analysis allows to evaluate rigorously the Sagnac effect, and the gravitational (Einstein) redshift.