Classification of Hypercylindrical Spacetimes with Momentum Flow

TL;DR

This paper classifies five-dimensional hypercylindrical spacetimes based on boost-invariant quantities, revealing three distinct types and suggesting some solutions may represent the end state of tachyonic matter collapse.

Contribution

It introduces a classification scheme for hypercylindrical spacetimes using boost-invariant measures, identifying new solution types and linking recent solutions to tachyonic matter collapse.

Findings

Identified three types of hypercylindrical geometries: ordinary, null, and tachyonlike strings.

Discovered two new vacuum solutions corresponding to null and tachyonlike strings.

Showed that recent extraordinary solutions are likely tachyonic and represent collapse endpoints.

Abstract

For the five-dimensional spacetimes whose four-dimensional sections are static, spherically symmetric ($SO(3)$) and flat asymptotically, we study the behavior of Arnowitt-Deser-Misner mass, tension and momentum densities characterizing such asymptotically hypercylindrical metrics under boosts along the cylindrical axis. For such stringlike metrics two boost-invariant quantities are found, which are a sort of "string rest mass-squared" and the sum of mass and tension densities. Analogous to the case of a moving point particle, we show that the asymptotically hypercylindrical geometries can be classified into three types depending on the value of the "string rest mass-squared", namely, "ordinary string", "null string" and "tachyonlike string" geometries. This asymptotic analysis shows that the extraordinary metrics reported recently by some of the authors belong to the tachyonlike string. Consequently, it is likely that such extraordinary solutions are the final states of tachyonic matter collapse. We also report two new vacuum solutions which belong to the null string and the tachyonlike string, respectively.