On gravitational wave-Cherenkov radiation from photons when passing through diffused dark matters

Analogy to Cherenkov radiation, when a particle moves faster than the propagation velocity of gravitational wave in matter ($v>c_{\rm{g}}$), we expect gravitational wave-Cherenkov radiation (GWCR). In the situation that a photon travels across diffuse dark matters, the GWCR condition is always satisfied, photon will thence loss its energy all the path. This effect is long been ignored in the practice of astrophysics and cosmology, without justification with serious calculation. We study this effect for the first time, and shows that this energy loss time of the photon is far longer than the Hubble time, therefore justify the practice of ignoring this effect in astrophysics context.