On the uniqueness of a shear-vorticity-acceleration-free velocity field in space-times

TL;DR

This paper proves the uniqueness of shear-vorticity-acceleration-free velocity fields in space-times, with specific exceptions, and explores their properties in four-dimensional space-times including implications for Einstein's equations.

Contribution

It establishes the conditions under which such velocity fields are unique in space-times, identifying special cases like warped and doubly twisted space-times.

Findings

Uniqueness of shear-vorticity-acceleration-free velocity fields in general space-times.

Exceptions include generalized Robertson-Walker and doubly twisted space-times.

In four dimensions, the Ricci and Weyl tensors are characterized, and Einstein equations relate to two perfect fluids.

Abstract

We prove that in space-times a velocity field that is shear, vorticity and acceleration-free, if any, is unique up to reflection, with these exceptions: generalized Robertson-Walker space-times whose space sub-manifold is warped, and twisted space-times (the scale function is space-time dependent) whose space sub-manifold is doubly twisted. In space-time dimension n = 4, the Ricci and the Weyl tensors are specified, and the Einstein equations yield a mixture of two perfect fluids.