Cylindrical sources in full Einstein and Brans-Dicke gravity

TL;DR

This paper investigates the applicability of a specific energy-momentum tensor used for cosmic strings in full Einstein and Brans-Dicke gravity, revealing limitations in static solutions within these theories.

Contribution

It demonstrates that the previously used energy-momentum tensor for cosmic strings cannot produce static solutions in full Einstein or Brans-Dicke gravity, highlighting its limitations.

Findings

The tensor used for cosmic strings does not admit static solutions in full Einstein gravity.

The tensor also fails to produce static solutions in Brans-Dicke gravity.

Most tensors in the considered family do not allow static solutions in these theories.

Abstract

It was shown by Hiscock that the energy-momentum tensor commonly used to model local cosmic strings in linearized Einstein gravity can be extended and used in the full theory, obtaining a metric in the exterior of the source with the same deficit angle. Here we show that this tensor is an exception within a family for which a static solution does not exist in full Einstein nor in Brans-Dicke gravity.