The LISA Time-Delay Interferometry Zero-Signal Solution. I: Geometrical Properties

Time-Delay Interferometry (TDI) is the data processing technique needed for generating interferometric combinations of data measured by the multiple Doppler readouts available onboard the three LISA spacecraft. Within the space of all possible interferometric combinations TDI can generate, we have derived a specific combination that has zero-response to the gravitational wave signal, and called it the {\it Zero-Signal Solution} (ZSS). This is a two-parameter family of linear combinations of the generators of the TDI space, and its response to a gravitational wave becomes null when these two parameters coincide with the values of the angles of the source location in the sky. Remarkably, the ZSS does not rely on any assumptions about the gravitational waveform, and in fact it works for waveforms of any kind. Our approach is analogous to the data analysis method introduced by G\"ursel & Tinto in the context of networks of Earth-based, wide-band, interferometric gravitational wave detectors observing in coincidence a gravitational wave burst. The ZSS should be regarded as an application of the G\"ursel & Tinto method to the LISA data.