Gravitational Metrological Triangle

Motivated by the similarity of the mathematical structure of Einstein's general relativity in its weak field limit and of Maxwell's theory of electrodynamics it is shown that there are gravitational analogs of the Josephson effect and the quantum Hall effect. These effects can be combined to derive a gravitational analogue of the electric quantum metrological triangle. The gravitational quantum metrological triangle may have applications in metrology and could be used to investigate the relation of the Planck constant to fundamental particle masses. This allows for quantum tests of the weak equivalence principle. Moreover, the similarity of the gravitational and the electric quantum metrological triangle can be used to test the universality of quantum mechanics.