On cosmic strings, infinite line-masses and conformal invariance

TL;DR

This paper explores a conformally invariant model of self-gravitating scalar-gauge fields in axially symmetric spacetime, revealing new features and constraints for matching vacuum and vortex solutions, with implications for higher-dimensional theories.

Contribution

It introduces a consistent conformal invariant Lagrangian for self-gravitating fields and analyzes its solutions in Bondi-Marder spacetime, highlighting the need for additional constraints and higher-dimensional models.

Findings

Exact vacuum solution with conformal factor in Bondi-Marder spacetime

Matching conditions impose constraints on vortex solutions

Potential extension to five-dimensional warped models

Abstract

We investigate the conformal invariant Lagrangian of the self-gravitating U(1) scalar-gauge field and find new features of the model on the time-dependent axially symmetric Bondi-Marder spacetime. By considering the conformal symmetry as exact at the level of the Lagrangian and broken in the vacuum, a consistent model is found with an exact solution of the vacuum Bondi-Marder spacetime $g_{\mu\nu}=\omega^2 \bar g_{\mu\nu}$, where $\omega$ is the conformal factor and $\bar g_{\mu\nu}$ the `un-physical` spacetime. If we try to match this vacuum solution onto the interior vortex solution of the coupled Einstein-scalar-gauge field, we need, besides the matching conditions, constraint equations in order to obtain a topological regular description of the small-scale behaviour of the model. Probably, one needs the five-dimensional warped counterpart model, where the 5D dilaton field act as a warp factor. Moreover, the tracelessness of the energy-momentum tensor could then be maintained by a contribution from the bulk.