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Results are presented from high-precision computations of the orbitalevolution and emitted gravitational waves for a stellar-mass object spiralinginto a massive black hole in a slowly shrinking, circular, equatorial orbit.The focus of these computations is inspiral near the innermost stable circularorbit (isco)---more particularly, on orbits for which the angular velocityOmega is 0.03 < Omega/Omega_{isco} < 1. The computations are based on theTeukolsky-Sasaki-Nakamura formalism, and the results are tabulated in a set offunctions that are of order unity and represent relativistic corrections tolow-orbital-velocity formulas. These tables can form a foundation for futuredesign studies for the LISA space-based gravitational-wave mission. A firstsurvey of applications to LISA is presented: Signal to noise ratios S/N arecomputed and graphed as functions of the time-evolving gravitational-wavefrequency for representative values of the hole's mass M and spin a and theinspiraling object's mass \mu, with the distance to Earth chosen to be r_o = 1Gpc. These S/N's show a very strong dependence on the black-hole spin, as wellas on M and \mu. A comparison with predicted event rates shows strong promisefor detecting these waves, but not beyond about 1Gpc if the inspiraling objectis a white dwarf or neutron star. This argues for a modest lowering of LISA'snoise floor. A brief discussion is given of the prospects for extractinginformation from the observed wavesComment: Physical Review D, in press; 21 pages, 9 figures, 10 tables it is  present in the RevTeX fil

Gravitational waves from a compact star in a circular, inspiral orbit, in the equatorial plane of a massive, spinning black hole, as observed by LISA