  The present article is the last in a series of five devoted to the study of
the effect of anisotropic pressure on the gravitationnal impact of a stationary
rigidly rotating cylindrically symmetric fluid with the use of new exact
solutions of General Relativity. In the four first papers in this series, three
kinds of pressures directed each along one of the principal stresses of the
fluid have been considered and new interior solutions of the field equations
have been constructed and analyzed. Here, key results and issues raised in
these previous works are synthesized and some fundamental notions of general
relativity, causality, regularity of Lorentzian manifolds, elementary flatness
in the vicinity of a symmetry axis, singularities, physics of angular deficits,
weak and strong energy conditions, are revisited. Then, a new derivation of the
corresponding dust solution is displayed and shown to correspond indeed to the
Lanczos-van Stockum solution shedding new light to this well-known spacetime.
