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 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