Note on the Levi-Civita metric - Halilsoy, M.; Mazharimousavi, S. Habib (World Scientific Publ Co Pte Ltd, 2022)
By introducing a new coordinate condition we divide the cylindrical spacetime of Levi-Civita (LC) into a sourceful inner (rho < rho(0) = const.) and vacuum outer (rho >= rho(0)) 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 rho = 0 the LC spacetime becomes 'Cartesian flat' so that no deficit angle arises.
Keywords: Levi-Civita metric; regular spacetime; exact solution