Among third-generation ground-based gravitational-wave detectors proposed for
the next decade, the Einstein Telescope provides a unique kind of null stream
$\unicode{x2014}$ the signal-free linear combination of data $\unicode{x2014}$
that enables otherwise inaccessible tests of the noise models. We project and
showcase challenges in modeling the noise in the 2030s and how it will affect
the performance of third-generation detectors. We find that the null stream of
the Einstein Telescope is capable of eliminating transient detector glitches
that are known to limit current gravitational-wave searches. The techniques we
discuss are computationally efficient and do not require a priori knowledge
about glitch models. Furthermore, we show how the null stream can be used to
provide an unbiased estimation of the noise power spectrum necessary for online
and offline data analyses even with multiple loud signals in the band. We
overview other approaches to utilizing the null stream. Finally, we comment on
the limitations and future challenges of null-stream analyses for the Einstein
Telescope and arbitrary detector networks.
