On cosmic strings, infinite line-masses and conformal invariance

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.

version 2. Layout improved and minor corrections. 15 pages; 7 figures. To present at the XI Black Hole workshop Lisbon, dec. 2018

References in corpus (1)

• A New Fate of a Warped 5D FRW Model with a U(1) Scalar Gauge Field