Some properties of the inertia tensor in Dixon’s theory

On the assumption that the Riemannian curvature and its variation over space–time are small enough and using an explicit expression for the inertia tensor defined by Dixon in his approach to describe the dynamics of extended bodies in general relativity, a proof of the semidefinite negative signature of the inertia tensor is given. Also, a coordinate evolution equation for the inertia tensor of an isolated extended body moving on a reference three-manifold is obtained.