The general theory of porcupines, perfect and imperfect

Abstract

Porcupines are networks of gravitational wave detectors in which the detectors and the distances between them are short relative to the gravitational wavelengths of interest. Perfect porcupines are special configurations whose sensitivity to a gravitational plane wave is independent of the propagation direction or polarization of the wave. I develop the theory of porcupines, including the optimal estimator \hat{h}^{ij} for the gravitational wave field; useful formulae for the spin-averaged and rotationally-averaged SNR^{2}; and a simple derivation of the properties of perfect porcupines. I apply these results to the interesting class of ``simple'' porcupines, and mention some open problems.