Universal 10 20 Hz stochastic gravitational waves from photon spheres of black holes

We show that photon spheres of supermassive black holes generate high-frequency stochastic gravitational waves through photon-graviton conversion. Remarkably, the frequency is universally determined as ${m}_{e}\sqrt{{m}_{e}/{m}_{p}}\ensuremath{\simeq}{10}^{20}\text{ }\text{ }\mathrm{Hz}$ in terms of the proton mass ${m}_{p}$ and the electron mass ${m}_{e}$. It turns out that the density parameter of the stochastic gravitational waves ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{gw}}$ could be ${10}^{\ensuremath{-}12}$. Since the existence of the gravitational waves from photon spheres is robust, it is worth seeking methods of detecting high-frequency gravitational waves around ${10}^{20}\text{ }\text{ }\mathrm{Hz}$.