Universal $10^{20}$Hz stochastic gravitational waves from photon spheres of black holes

Abstract

We show that photon spheres of supermassive black holes generate high-frequency stochastic gravitational waves through the photon-graviton conversion. Remarkably, the frequency is universally determined as $m_e\sqrt{m_e/m_p}\simeq 10^{20}\text{Hz}$ 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 ${\Omega }_{\text{gw}}$ could be $10^{-12}$. Since the existence of the gravitational waves from photon spheres is robust, it is worth seeking methods of detecting high-frequency gravitational waves around $10^{20}$Hz.

6 pages, 2 figures

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