Analogy between general relativity and electromagnetism for slowly moving particles in weak gravitational fields

Starting from the equations of general relativity, equations similar to those of electromagnetic theory are derived. It is assumed that the particles are slowly moving (v≪c), and the gravitational field is sufficiently weak that nonlinear terms in Einstein’s field equations can be neglected. For static fields, the analogy to electrostatics and magnetostatics is very close. Results are compared with those of a previous derivation by Braginsky, Caves, and Thorne [Phys. Rev. D 15, 2047–2068 (1977)]. These results lead to very simple derivations of the Lense–Thirring precession [Phys. Z. 19, 156–163 (1918)] and the spin‐curvature force of Papepetrou [Proc. R. Soc. London Ser. A 209, 248–258 (1951)] and Pirani [Acta Phys. Pol. 15, 389–405 (1956)].