Prospects for detection of ultra high frequency gravitational waves from compact binary coalescenses 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 formulas encountered in the literature are revised. In particular, we carefully take into account the fast drift of the gravitational wave frequency and the relevant experimental timescales. We also relax the usual assumption that only the merging phase should be considered. The distances that can be probed and expected event rates are carefully evaluated, taking into account degeneracies between physical parameters. We show where experimental efforts should be focused to improve the sensitivity and we conclude that any detection in the near future is extremely unlikely.