When two black holes merge far away, we receive a tremor of space — gravitational waves. Usually, they are described by Einstein's equations, but what if gravity works differently at the tiniest distances? The authors took one such hypothesis — Hořava–Lifshitz gravity. In it, a term with the fourth power of the wave number (k⁴) is added to the familiar wave equation. It's as if a stretched string, besides its usual elasticity, gained an extra stiffness noticeable only at very rapid oscillations.
It turns out that such an addition does not break the shape of the waves: the two standard polarizations (“plus” and “cross”) are preserved, do not mix, and do not split by helicity. But the signal's amplitude and phase begin to depend on frequency. The higher the frequency, the stronger the correction. For a pair of black holes on a circular orbit, this means that the gravitational wave signal reaches us slightly quieter and with a small time shift, like an echo that not only fades but also slightly changes its pitch.
The scientists derived formulas for the energy flux and total luminosity of such a system, as well as for the gradual increase in signal frequency — the so-called chirp. Comparing with the GWTC-4.0 catalog, they obtained a constraint on the parameter α: from –620 to +190 in units of inverse square electronvolt. This means that if the extra stiffness of space exists, it is very small, but already not zero within measurement accuracy.
LIGO detectors sense mirror displacements of thousandths of a proton diameter — roughly like the distance to the nearest star changing by the thickness of a human hair.
In Carl Sagan's novel "Contact," the heroine hears a rhythmic signal from space that turns out to be a message from an alien civilization encoded in the modulation of gravitational waves.