Prospects for detection of ultra high frequency gravitational waves from hyperbolic encounters with resonant cavities

In this brief article, we pursue the systematic investigation of possible gravitational wave sources in the gigahertz band. We focus on hyperbolic encounters of light black holes and evaluate precisely the expected signal when accounting for the detailed characteristics of haloscope experiments. Considering the GraHal setup as a benchmark, we insist on the correct signal-to-noise ratio expression, taking into account the appropriate timescales resulting from both physical and instrumental constraints. The associated maximum distance - of the order of a hundredth of an astronomical unit - at which an event can be detected is calculated for optimal, suboptimal, and general trajectories. The main conclusion is that detection seems clearly out of reach.