Relation between quasirigidity and L-rigidity in space-times of constant curvature and weak fields

Abstract

The relation between quasirigidity and L-rigidity in space-times of constant nonzero curvature and in space-times with small curvature (weak fields) is studied. The covariant expansion of bitensors about a point is considered. We obtain an increase in the order of magnitude, under L-rigidity conditions, of the rate of change with respect to a comoving orthonormal frame of the linear momentum, angular momentum, and reduced multipole moments of the energy-momentum tensor. Thus, L-rigidity leads to quasirigidity in such space-times.