Multiple mode gravitational wave detection with a spherical antenna

Apart from being omnidirectional, a solid elastic sphere is a natural multimode and multifrequency device for the detection of gravitational waves (GW). Motion sensing in a spherical GW detector thus requires a multiple set of transducers attached to it at suitable locations. If these are resonant then they exert a significant back action on the larger sphere and, as a consequence, the joint dynamics of the entire system must be properly understood before reliable conclusions can be drawn from data obtained using this system . In this paper, I present and develop an analytical approach to the study of such dynamics, which generalizes the currently existing ones and clarifies their actual range of validity. In addition, the new formalism shows that resonator layouts exist that are alternatives to the highly symmetric Truncated Icosahedron Gravitational Antenna (TIGA) , and that they have potentially interesting properties. I will describe in detail one resonance layout that has mode channels , only requires five resonators per quadrupole-mode sensed and is based on a Pentagonal HexaContrahedron (PHC) polyhedric shape. Also, the perturbative nature of the proposed approach makes it very well adapted to systematically assessing the consequences of realistic mistunings in the device parameters, by robust analytic methods. In order to check the real value of the mathematical model, its predictions have been compared with experimental data from the Louisiana State University (LSU) prototype detector TIGA and agreement between the predictions and data is consistently found to reach a satisfactory precision of four decimal places.