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Spinning cosmic strings in conformal gravity

Reinoud Jan slagter

http://orcid.org/0000-0002-2429-9866

Asfyon, Astronomisch Fysisch Onderzoek Nederland, The Netherlands

University of Amsterdam, The Netherlands

E-mail Address: info@asfyon.com

Corresponding author.

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and

Christopher Levi Duston

Physics Department, Merrimack College, N Andover, MA, USA

E-mail Address: dustonc@merrimack.edu

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https://doi.org/10.1142/S0217751X20500244Cited by:0 (Source: Crossref)

Abstract

We investigate the space–time of a spinning cosmic string in conformal invariant gravity, where the interior consists of a gauged scalar field. We find exact solutions of the exterior of a stationary spinning cosmic string, where we write the metric as $g_{μ ν} = ω^{2} {\tilde{g}}_{μ ν}$ , with $ω$ a dilaton field which contains all the scale dependences. The “unphysical” metric ${\tilde{g}}_{μ ν}$ is related to the $(2 + 1)$ -dimensional Kerr space–time. The equation for the angular momentum $J$ decouples, for the vacuum situation as well as for global strings, from the other field equations and delivers a kind of spin-mass relation. For the most realistic solution, $J$ falls off as $\sim \frac{1}{r}$ and $\partial_{r} J \to 0$ close to the core. The space–time is Ricci flat. The formation of closed timelike curves can be pushed to space infinity for suitable values of the parameters and the violation of the weak energy condition can be avoided. For the interior, a numerical solution is found. This solution can easily be matched at the boundary on the exterior exact solution by special choice of the parameters of the string. This example shows the power of conformal invariance to bridge the gap between general relativity and quantum field theory.

Keywords:

PACS: 04.20.Jb, 04.50.Gh, 04.25.dg, 11.27.+d, 11.15.Ex, 11.25.Hf, 98.80.Cq

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