Note on the Levi-Civita metric

Abstract

By introducing a new coordinate condition we divide the cylindrical spacetime of Levi-Civita (LC) into a sourceful inner ([Formula: see text]) and vacuum outer ([Formula: see text]) regions. The emergent fluid with zero radial pressure confined to the finely-tuned inner region serves to make the spacetime regular in a natural way. At [Formula: see text] the LC spacetime becomes ‘Cartesian flat’ so that no deficit angle arises.