Spherical gravitational wave antennas and the truncated icosahedral arrangement

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Abstract
A spherical gravitational wave detector can be equally sensitive to a wave from any direction, and also can be able to measure its direction and polarization. We derive a set of equations to describe the mechanics of a spherical antenna coupled to an arbitrary number of attached mechanical resonators. A special arrangement of six resonators is proposed, which we term a truncated icosahedral gravitational wave antenna. An analytic solution to the equations of motion is found for this case. We find that direct deconvolution of the gravitational tensor components can be accomplished with a specified set of linear combinations of the resonator outputs, which we call the mode channels. We develop one simple noise model for this system and calculate the resulting strain noise spectrum. We conclude that the angle-averaged energy sensitivity will be 56 times better than for the typical equivalent bar-type antenna with the same noise temperature. DOI: http://dx.doi.org/10.1103/PhysRevD.51.2546 © 1995 The American Physical Society