General relativistic treatment of LISA optical links

LISA is a joint space mission of the NASA and the ESA for detecting low-frequency gravitational waves in the band 10-5 to 1 Hz. In order to attain the requisite sensitivity for LISA, the laser frequency noise must be suppressed below the other secondary noises such as the optical path noise, acceleration noise, etc. This is achieved by the technique called time delay interferometry (TDI) in which the data are combined with appropriate time delays. In this paper we approximately compute the spacecraft orbits in the gravitational field of the Sun and Earth. We have written a numerical code which computes the optical links (time delays) in the general relativistic framework within an accuracy of ~10 m, which is sufficient for TDI. Our computation of the optical links automatically takes into account the effects such as the Sagnac, Shapiro delay, etc. We show that by optimizing LISA orbits, and using the symmetries inherent in the configuration of LISA and in the physics, the residual laser noise in the modified first-generation TDI can be adequately suppressed. We demonstrate our results for some important TDI observables