On the Levi-Civita solutions with cosmological constant

TL;DR

This paper investigates Levi-Civita solutions with a cosmological constant, analyzing their properties, extensions, and the conditions under which they form geodesically complete spacetimes or black hole structures with plane symmetry.

Contribution

It provides a detailed study of Levi-Civita solutions with cosmological constant, including extensions leading to black hole structures and classification of spacetime types.

Findings

Some solutions require extension for geodesic completeness.

Extensions can produce black hole structures with plane symmetry.

Non-complete spacetimes are Petrov type D, others are Petrov type I.

Abstract

The main properties of the Levi-Civita solutions with the cosmological constant are studied. In particular, it is found that some of the solutions need to be extended beyond certain hypersurfaces in order to have geodesically complete spacetimes. Some extensions are considered and found to give rise to black hole structure but with plane symmetry. All the spacetimes that are not geodesically complete are Petrov type D, while in general the spacetimes are Petrov type I.