Analogy between general relativity and electrodynamics for slowly moving particles in weak gravitational field, Edward G. Harris, Am. J. Phys., 59(5), May 1991
Starting from the equations of general relativity, equations similar to those of the electromagnetic theory are derived. It is assumed that the particles are slowly moving (v << c), and the gravitational field is sufficiently weak that non-linear terms in Einstein's 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 (1997)]. 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)].