Junction conditions in general relativity with spin sources

Alex Giacomini, Ricardo Troncoso, and Steven Willison
Phys. Rev. D 73, 104014 – Published 11 May 2006

Abstract

The junction conditions for general relativity in the presence of domain walls with intrinsic spin are derived in three and higher dimensions. A stress tensor and a spin current can be defined just by requiring the existence of a well-defined volume element instead of an induced metric, so as to allow for generic torsion sources. In general, when the torsion is localized on the domain wall, it is necessary to relax the continuity of the tangential components of the vielbein. In fact it is found that the spin current is proportional to the jump in the vielbein and the stress-energy tensor is proportional to the jump in the spin connection. The consistency of the junction conditions implies a constraint between the direction of flow of energy and the orientation of the spin. As an application, we derive the circularly symmetric solutions for both the rotating string with tension and the spinning dust string in three dimensions. The rotating string with tension generates a rotating truncated cone outside and a flat space-time with inevitable frame dragging inside. In the case of a string made of spinning dust, in opposition to the previous case no frame dragging is present inside, so that in this sense, the dragging effect can be shielded by considering spinning instead of rotating sources. Both solutions are consistently lifted as cylinders in the four-dimensional case.

  • Received 21 March 2006

DOI:https://doi.org/10.1103/PhysRevD.73.104014

©2006 American Physical Society

Authors & Affiliations

Alex Giacomini*, Ricardo Troncoso, and Steven Willison

  • Centro de Estudios Científicos (CECS), Casilla 1469, Valdivia, Chile

  • *Electronic address: giacomini@cecs.cl
  • Electronic address: ratron@cecs.cl
  • Electronic address: steve@cecs.cl

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Issue

Vol. 73, Iss. 10 — 15 May 2006

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