Analytic results for the gravitational radiation from a class of cosmic string loops

Bruce Allen, Paul Casper, and Adrian Ottewill
Phys. Rev. D 50, 3703 – Published 15 September 1994
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Abstract

Cosmic string loops are defined by a pair of periodic functions a and b, which trace out unit-length closed curves in three-dimensional space. We consider a particular class of loops, for which a lies along a line and b lies in the plane orthogonal to that line. For this class of cosmic string loops one may give a simple analytic expression for the power γ radiated in gravitational waves. We evaluate γ exactly in closed form for several special cases: (1) b a circle traversed M times; (2) b a regular polygon with N sides and interior vertex angle π-2πM/N; (3) b an isosceles triangle with semiangle θ. We prove that case (1) with M=1 is the absolute minimum of γ within our special class of loops, and identify all the stationary points of γ in this class.

  • Received 26 April 1994

DOI:https://doi.org/10.1103/PhysRevD.50.3703

©1994 American Physical Society

Authors & Affiliations

Bruce Allen and Paul Casper

  • Department of Physics, University of Wisconsin–Milwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201

Adrian Ottewill

  • Department of Mathematical Physics, University College Dublin, Belfield, Dublin 4, Ireland

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Issue

Vol. 50, Iss. 6 — 15 September 1994

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