Post Newtonian Rigid Body

TL;DR

This paper develops the first complete post-Newtonian model of a rigid body, extending classical relations to include relativistic corrections, with potential applications in geodynamics and astronomy.

Contribution

It introduces a novel constraint on mass current density and density to construct a comprehensive post-Newtonian rigid body model, extending classical relations.

Findings

Derived the post-Newtonian relation between mass quadrupole moment and moment of inertia tensor.

Extended classical rigid body relations to include relativistic corrections.

Reduced to Newtonian model when relativistic terms are neglected.

Abstract

In this paper, it is the first time to construct a complete post-Newtonian (PN) model of a rigid body by means of a new constraint on the mass current density and mass density. In our PN rigid body model most of relations, such as spin vector proportional to the angular velocity, the definition on the moment of inertia tensor, the key relation between the mass quadrupole moment and the moment of inertia tensor, rigid rotating formulae of mass quadrupole moment and the moment of inertia tensor, are just the extension of the main relations in Newtonian rigid body model. When all of $1/c^2$ terms are neglected, the PN rigid body model and the corresponding formulae reduce to Newtonian version. The key relation is obtained in this paper for the first time, which might be very useful in the future application to problems in geodynamics and astronomy.