ANALYTIC RESULTS FOR THE GRAVITATIONAL-RADIATION FROM A CLASS OF COSMIC-STRING LOOPS

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 gamma radiated in gravitational waves. We evaluate gamma 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 pi - 2 pi M/N; (3) b an isosceles triangle with semiangle theta. We prove that case (1) with M = 1 is the absolute minimum of gamma within our special class of loops, and identify all the stationary points of gamma in this class.