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In the years 1917-1919 Tullio Levi-Civita published a number of papers presenting new solutions to Einsteins equations. This work, while partially translated, remains largely inaccessible to English speaking authors. In this paper we review these solutions, and present them in a modern, readable manner. We will also compute both Cartan-Karlhede and Carminati-Mclenaghan invariants such that these solutions are invariantly characterized by two distinct methods. These methods will allow for these solutions to be totally, and invariantly characterized. Because of the variety of solutions considered here, this paper will also be a useful reference for those seeking to learn to apply the Cartan-Karlhede algorithm in practice.
Applying the Pomeransky inverse scattering method to the four-dimensional vacuum Einstein equation and using the Levi-Civita solution for a seed, we construct a cylindrically symmetric single-soliton solution. Although the Levi-Civita spacetime gener
Applying the Pomeransky inverse scattering method to the four-dimensional vacuum Einstein equations and using the Levi-Civita solution as a seed, we construct a two-soliton solution with cylindrical symmetry. In our previous work, we constructed the
We study the most general solution for affine connections that are compatible with the variational principle in the Palatini formalism for the Einstein-Hilbert action (with possible minimally coupled matter terms). We find that there is a family of s
We consider an exact Einstein-Maxwell solution constructed by Alekseev and Garcia which describes a Schwarzschild black hole immersed in the magnetic universe of Levi-Civita, Bertotti and Robinson (LCBR). After reviewing the basic properties of this
The quasi-spherical Szekeres dust solutions are a generalization of the spherically symmetric Lemaitre-Tolman-Bondi dust models where the spherical shells of constant mass are non-concentric. The quasi-spherical Szekeres dust solutions can be conside