Prospects for detection of ultra high frequency gravitational waves from compact binary coalescences with resonant cavities

This article aims at clarifying the situation about astrophysical sources that might be observed with haloscope experiments sensitive to gravitational waves in the 1–10 GHz band. The GrAHal setup is taken as a benchmark. We follow a very pedagogical path so that the full analysis can easily be used by the entire community who might not be familiar with the theoretical framework. Different relevant physical regimes are considered in details and some approximations encountered in the literature are questioned. In particular, we carefully take into account the fast drift of the gravitational wave frequency and the associated experimental limitations of different kinds. This has strong impact on sensitivity estimates. We also relax the usual assumption that only the merging phase should be considered. The distances that can be probed are carefully evaluated, taking into account degeneracies between physical parameters. We conclude that any detection in the near future is probably impossible.