Post-Newtonian quasirigid body

In this paper, we construct for the first time, in the first post-Newtonian (1PN) approximation, a complete model of a quasirigid body by means of a new constraint on the mass current density and mass density. In our 1PN quasirigid body model most of the relations, such as the spin vector proportional to the angular velocity, the definition of the moment of inertia tensor, the key relation between the mass quadrupole moment and the moment of inertia tensor, the rigid rotating formulas for the mass quadrupole moment, and the moment of inertia tensor, are just an extension of the main relations in the Newtonian rigid body model. When all of the 1/c² terms are neglected, the 1PN quasirigid body model and the corresponding formulas reduce to the Newtonian version. A key relation is obtained in this paper for the first time, which might be very useful in future applications to problems in geodynamics and astronomy.