Atomic electron transitions of hydrogen-like atoms induced by gravitational waves

As a realistic model of a quantum system of matter, this paper investigates the gravitational-wave effects on a hydrogen-like atom using a first-principles approach. By formulating the tetrad formalism of linearized gravity, we naturally incorporate gravitational-wave effects through minimal coupling in the covariant Dirac equation. The atomic electron transition rates induced by the gravitational wave are calculated using first-order perturbation theory, revealing a distinctive selection rule along with Fermi's golden rule. This rule can be elegantly understood in terms of gravitons as massless spin-2 particles. Our results suggest the existence of gravitons and may lead to a novel approach to probing ultra-high-frequency gravitational waves.