On admissible motions in a given space-time

Abstract

Given the four-velocityV describing the motion of a continuous medium, the covariant derivativeg(V) may be uniquely decomposed in terms of the vorticity tensor Ω, the expansion tensorK, and the four-accelerationC. In the present paper we examine the integrability conditions on the fields Ω,K, andC ensuring the existence of a four-velocity fieldV.