A 1+5-dimensional gravitational-wave solution: curvature singularity and spacetime singularity

TL;DR

This paper presents a 1+5-dimensional gravitational-wave solution with two curvature singularities, demonstrating that not all curvature singularities necessarily indicate spacetime singularities, through an extension that removes one such singularity.

Contribution

It introduces a specific higher-dimensional gravitational-wave solution and shows how a curvature singularity can be removed, challenging the notion that all curvature singularities are spacetime singularities.

Findings

One curvature singularity can be removed by spacetime extension.

Curvature singularities are not always indicative of spacetime singularities.

The solution exemplifies the distinction between curvature and spacetime singularities.

Abstract

We solve a $1+5$-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities.