Slow stationary sources

The linearized theory is applied to sources such as ordinary stars whose speed is small compared to the speed of light. This yields the “gravitoelectromagnetic” theory. The gravitoelectromagnetic field equations are obtained, along with their general solution via scalar and vector potentials. It is shown how to calculate the metric perturbation, and hence the field, due to a rotating ring or a ball, and thus how to calculate orbits, timing, and the Lense-Thirring precession.