An Invariant Characterization of the Levi-Civita Spacetimes

In the years 1917–1919 Tullio Levi-Civita published a number of papers presenting new exact solutions to Einstein’s equations. These works, while partially translated, remains largely inaccessible to English speaking researchers. Furthermore, the age and structures of these papers have often resulted in more contemporary works citing these papers in confusing or incorrect ways. It is not uncommon to find the series of Levi-Civita's papers cited by the general heading of the entire series or by referencing to only the first article in the series. Here, we clarify the structure of Levi-Civita's works on exact solutions that are of current interest. We review and characterize these solutions and their properties. We present them in a modern readable manner as well as show a new additional alternative form to one solution.