High-frequency gravitational waves (MHz-GHz) are predicted by many beyond-Standard-Model scenarios - mergers of planetary-mass primordial black holes, black-hole superradiance, early-Universe phase transitions - yet no detector in this band has demonstrated a scientifically credible detection capability. Two source records define the problem. The rare transient events reported in 2021 from a cryogenic bulk-acoustic-wave (BAW) antenna were shown by Lasky and Thrane to be incompatible with a gravitational-wave origin: the implied stochastic energy density is about 10810^{8} times larger than cosmology permits, and the low-frequency memory signal accompanying any such burst would have been unmistakable in LIGO/Virgo; the terrestrial origin of those events remains unidentified, and roughly four orders of magnitude in strain sensitivity are needed before a positive BAW detection would even be self-consistent (implying Ωgw≲1\Omega_{\rm gw}\lesssim1). Separately, the proposed quarterly split-cavity electromagnetic-conversion detector reaches its projected strain sensitivity h∼10−20h\sim10^{-20} near 10 MHz only under a simplified thermal-noise-only assumption, with event-rate and directionality forecasts and strong-magnet implementation left open. The combined problem - establishing artifact-rejected, noise-validated, physically self-consistent detection capability for high-frequency gravitational waves, with no detector-type restriction - remains open as of August 2026: multi-detector coincidence analysis has now been demonstrated and excludes 2021-type events as non-gravitational background, but no MHz-GHz detector approaches the required sensitivity, and complete noise models and source forecasts for proposed schemes are still missing.

Background

Gravitational waves (GWs) are propagating strain perturbations of spacetime. All direct detections to date - by the LIGO, Virgo and KAGRA laser interferometers - lie in the audio band (roughly 10-1000 Hz) and come from merging black holes and neutron stars. A substantial international effort targets much higher frequencies, from MHz to GHz, where known astrophysical sources within the Standard Model are essentially absent; a real signal in this band would therefore most likely signal beyond-Standard-Model physics, such as mergers of primordial black holes (PBHs, hypothetical black holes formed in the early Universe), graviton emission from axion clouds grown around spinning black holes by the superradiance instability (the exponential amplification of a boson field that extracts rotational energy from a spinning black hole), or relics of early-Universe phase transitions. Two community white papers (Aggarwal et al. 2021, 2025) review the candidate sources and the proposed detectors.

Two detector families anchor the present problem. The first is the resonant-mass antenna: a bulk acoustic wave (BAW) resonator is a cryogenic piezoelectric quartz device in which a passing GW would resonantly excite high-overtone acoustic modes, the vibration being converted by the piezoelectric effect into an electrical signal. A quartz BAW device operated at low temperature by Goryachev et al. (2021) recorded two rare, strong transient excitations - on 12 May 2019 in a single monitored mode at 5.506 MHz, and on 27 November 2019 simultaneously in modes at 5.506 and 4.993 MHz - during 153 days of running, with no correlation found in available environmental records; the authors listed mundane possibilities (e.g. cosmic rays, meteor activity) alongside exotic ones including GWs. The second family is electromagnetic conversion: by the inverse Gertsenshtein effect, a GW crossing a strong static magnetic field is partially converted into an electromagnetic wave - photon-graviton mixing closely related to the mechanism exploited by axion haloscopes (resonant microwave-cavity experiments built to detect axion dark matter). Gao, Gao, Liu and Sun (2024) proposed a quarterly split cavity - a cylindrical cavity whose wall is split into four electrically separated quadrants, read out through an inductor-capacitor (LC) resonant circuit - inside a roughly 14 Tesla magnet, projecting narrowband strain sensitivity h∼10−20⋅(106/Q)h\sim10^{-20}\cdot(10^{6}/Q) (with QQ the resonance quality factor) and broadband sensitivity h∼10−13h\sim10^{-13} near 10 MHz for a meter-sized cavity, but explicitly under a simplified, thermal-noise-only noise assumption.

The credibility question crystallized when Lasky and Thrane (2021) showed that the 2021 BAW events cannot be gravitational waves. First, a GW origin would imply an integrated gravitational-wave energy density Ωgw≈108\Omega_{\rm gw}\approx10^{8}, where Ωgw\Omega_{\rm gw} is the GW energy density per logarithmic frequency interval divided by the critical density needed to close the Universe; basic cosmology requires Ωgw≪1\Omega_{\rm gw}\ll1, so the inferred value is unphysical even after allowing model uncertainties of factors of several and Poisson counting uncertainty. Second, any anisotropic GW burst is followed by a permanent strain offset (gravitational-wave memory); the low-frequency 'orphan memory' burst accompanying the BAW events would have appeared in LIGO/Virgo with signal-to-noise ratio ρ≳106\rho\gtrsim10^{6}, and no such bursts were seen. Lasky and Thrane concluded that the BAW antenna's characteristic-strain sensitivity (characteristic strain hch_{c} is the strain amplitude scaled by the square root of the number of wave cycles, the standard quantity for comparing detector sensitivities across signal durations) must improve by roughly four orders of magnitude before a positive detection would imply Ωgw≲1\Omega_{\rm gw}\lesssim1 - that is, before a detected event would even be energetically self-consistent. This defines the problem: in this band, scientific credibility of a detection claim is not automatic - the claim must survive demonstrated rejection of terrestrial artifacts, rest on a complete noise model, and be physically self-consistent in its inferred energy budget.

Problem Statement

The problem is to make high-frequency (MHz-GHz) gravitational-wave detection scientifically credible, with no restriction on detector type (resonant-mass antennas, electromagnetic-cavity conversion devices, or other concepts). This requires establishing, for a detector of any type, a strain sensitivity that follows from a complete noise model and whose threshold event would satisfy the self-consistency condition below, together with the artifact-rejection methodology that establishes terrestrial-origin exclusion. As the source literature makes explicit, a claimed detection in this band is scientifically credible only if it survives demonstrated rejection of terrestrial artifacts and rests on a validated, physically self-consistent sensitivity. (1) Artifact rejection: candidate transient events must have terrestrial/instrumental origins excluded, so that events like the 2021 BAW transients, whose mundane cause is still unidentified even though their gravitational-wave interpretation is refuted, can be classified as background by demonstrated methodology rather than by argument. (2) A validated noise budget and self-consistent sensitivity: the detector's strain sensitivity must follow from a complete noise model (thermal noise together with amplifier backaction, quantum noise, and bandwidth limits - not a thermal-only assumption as in the split-cavity proposal), and it must be sufficient that a positive detection would be physically self-consistent: a threshold detected event must imply Ωgw≲1\Omega_{\rm gw}\lesssim1 for a stated benchmark source population - the check may adopt the event rate and energy budget that Lasky and Thrane used to infer Ωgw≈108\Omega_{\rm gw}\approx10^{8} from the BAW events, without any forecast of the true source rate - and be compatible with audio-band orphan-memory constraints. For the BAW antenna this is the roughly four-orders-of-magnitude characteristic-strain improvement; for cavity conversion schemes the analogous self-consistency requirement applies. Event-rate and sky-directionality estimates for the plausible candidate sources, which the split-cavity proposal explicitly left to future work, remain an open ingredient of search design in this band rather than a condition on the credibility of a detection itself.

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