Gravitomagnetic Field and Time-Dependent Spin-Rotation Coupling

The Kerr metric of spherically symmetric gravitational field is analyzed through the coordinate transformation from the rotating frame to fixing frame, and consequently that the inertial force field (with the exception of the centrifugal force field) in the rotating system is one part of its gravitomagnetic field is verified. We investigate the spin-rotation coupling and, by making use of Lewis-Riesenfeld invariant theory, we obtain exact solutions of the Schr\"{o}dinger equation of a spinning particle in a time-dependent rotating reference frame. A potential application of these exact solutions to the investigation of Earth$^{,}$s rotating frequency fluctuation by means of neutron-gravity interferometry experiment is briefly discussed in the present paper.