Waveforms for Gravitational Radiation from Cosmic String Loops

TL;DR

This paper derives general formulas for gravitational waveforms emitted by cosmic string loops, focusing on piecewise linear loops, and explores their properties and relations to smooth loops.

Contribution

It provides explicit waveform formulas for cosmic string loops, especially piecewise linear ones, and analyzes their characteristics and approximations.

Findings

Waveforms are piecewise linear functions for piecewise linear loops.

Explicit examples of gravitational waveforms are provided.

Relations between smooth and piecewise linear loop radiation are discussed.

Abstract

We obtain general formulae for the plus- and cross- polarized waveforms of gravitational radiation emitted by a cosmic string loop in transverse, traceless (synchronous, harmonic) gauge. These equations are then specialized to the case of piecewise linear loops, and it is shown that the general waveform for such a loop is a piecewise linear function. We give several simple examples of the waveforms from such loops. We also discuss the relation between the gravitational radiation by a smooth loop and by a piecewise linear approximation to it.