Beyond point-particle approx. In the geodesic approximation,the compact object is taken as a point particle without internal structure.This is certainly not true. This problem has been discussed long time ago,first by M.Mathisson (1937)in an ambitious paper "Neue mechanik materieller systemes",Acta Phys.Polon 6 (1937)163-2900. ("New mechanics of material systems",Republication,Gen.Rel.Grav. 42(2010)1011-1048.) 口卡4三色至习QC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Beyond point-particle approx. In the geodesic approximation, the compact object is taken as a point particle without internal structure. This is certainly not true. This problem has been discussed long time ago, first by M. Mathisson (1937) in an ambitious paper “Neue mechanik materieller systemes”, Acta Phys. Polon 6 (1937)163-2900. (“New mechanics of material systems”, Republication, Gen.Rel.Grav. 42(2010)1011-1048.) Some years later, A. Papapetrou (1951) addressed this issue. “Spinning test particle in general relativity, 1”, Proc. Roy. Soc. Lond. A209(1951)248-258. The modern version was developed by W.G. Dixon in a series of papers in 1970s. He completed Mathisson’s formalism to discuss the dynamics of extended bodies in GR beyond the dipole and quadrupole approx.. This resulted in the so-called Mathisson-Papapetrou-Dixon (MPD) equations