Time-delay interferometry and the relativistic treatment of LISA optical links

LISA is a joint space mission of the ESA and NASA for detecting low frequency gravitational radiation in the band $10^{-5} - 1$ 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 because of the redundancy in the data, more specifically, by combining six appropriately time-delayed data streams containing fractional Doppler shifts - time delay interferometry (TDI). The orbits of the spacecraft are computed in the gravitational field of the Sun and Earth in the Newtonian framework, while the optical links are treated fully general relativistically and thus, effects such as the Sagnac, Shapiro delay, etc. are automatically incorporated. We show that in the model of LISA that we consider here, there are symmetries inherent in the physics, which may be used effectively to suppress the residual laser frequency noise and simplify the algebraic approach to TDI.