Levi-Civita spacetimes in multidimensional theories

TL;DR

This paper derives the most general static cylindrically symmetric vacuum solutions in higher-dimensional Einstein gravity, exploring their properties and interpretations in lower dimensions, including scalar-vacuum and braneworld scenarios.

Contribution

It presents the first comprehensive family of Levi-Civita-Kasner solutions in higher dimensions and analyzes their dimensional reduction and physical interpretations.

Findings

Derived the most general static cylindrically symmetric vacuum solutions in (4+N) dimensions.

Constructed a family of Levi-Civita-Kasner solutions under separation of variables.

Showed these solutions can be interpreted as scalar-vacuum or braneworld spacetimes.

Abstract

We obtain the most general static cylindrically symmetric vacuum solutions of the Einstein field equations in $(4 + N)$ dimensions. Under the assumption of separation of variables, we construct a family of Levi-Civita-Kasner vacuum solutions in $(4 + N)$. We discuss the dimensional reduction of the static solutions. Depending on the reduction procedure, they can be interpreted either as a scalar-vacuum generalization of Levi-Civita spacetimes, or as the effective 4D vacuum spacetime outside of an idealized string in braneworld theory.