Gravitational-wave interferometers are expected to monitor the last three minutes of inspiral and final coalescence of neutron star and black hole binaries at distances approaching cosmological, where the event rate may be many per year. Because the binary's accumulated orbital phase can be measured to a fractional accuracy <^C 10~3 and relativistic effects are large, the wave forms will be far more complex and carry more information than has been expected. Improved wave form modeling is needed as a foundation for extracting the waves' information, but is not necessary for wave detection.

A particle of mass p moves, in the absence of external forces, in the geometry of a nonrotating black hole of mass M. The system (black hole plus particle) emits gravitational waves, and the particle's orbit evolves under radiation reaction. The aim of this paper is to calculate this evolution Our calculations are carrled out under the assumptions that g / M << 1, that the orbit is bound, and that radiation reaction takes place over a time scale much longer than the orbital period. The bound orbits of the Schwarzschild spacetime can be fully characterized, apart from initial conditions, by two orbital parameters: the semi-latus rectum p. and the eccentricity c. These parameters are so defined that the turning points of the radial motion (the values of the Schwarzschild radial coordinate at which the radial component of the four-velocity vanishes) are given by TI = p M l ( 1 + e ) and rz = p M l ( 1 -e). The units are such that G = c = 1. We use the Teukolsky perturbation formalism to calculate the rates at which the gravitational waves generated by the orbiting particle remove energy and angular momentum from the system. These are then related to the rates of change of p and e, which determine the orbital evolution. We find that the radiation reaction continually decreases p, in such a way that the particle eventually plunges inside the black hole. Plunging occurs when p becomes smaller than 6 + 2e. (Orbits for which p . , 6 + 2e do not have a turning point at r = rl.) For weak-field, slow-motion orbits (which are characterized by large values of p), the radiation reaction decreases e also. However, for strong-field, fast-motion orbits (small values of p). the radiation reaction zncreases the eccentricity if p is sufficiently close to its minimum value 6 + 2e.

We present a new approximate method for constructing gravitational radiation driven inspirals of test bodies orbiting Kerr black holes. Such orbits can be fully described by a semilatus rectum p, an eccentricity e, and an inclination angle , or, by an energy E, an angular momentum component L z , and a third constant Q. Our scheme uses expressions that are exact ͑within an adiabatic approximation͒ for the rates of change (ṗ ,ė ,) as linear combinations of the fluxes (Ė ,L z ,Q ), but uses quadrupole-order formulas for these fluxes. This scheme thus encodes the exact orbital dynamics, augmenting it with an approximate radiation reaction. Comparing inspiral trajectories, we find that this approximation agrees well with numerical results for the special cases of eccentric equatorial and circular inclined orbits, far more accurate than corresponding weak-field formulas for (ṗ ,ė ,). We use this technique to study the inspiral of a test body in inclined, eccentric Kerr orbits. Our results should be useful tools for constructing approximate waveforms that can be used to study data analysis problems for the future Laser Interferometer Space Antenna gravitational-wave observatory, in lieu of waveforms from more rigorous techniques that are currently under development. I. BACKGROUND AND MOTIVATIONThe capture of stellar-mass compact objects by massive black holes residing in galactic nuclei is expected to be one of the most important sources of gravitational radiation for the future Laser Interferometer Space Antenna ͑LISA͒ spacebased detector ͓1,2͔. Observing such events will provide information about stellar dynamics in galactic nuclei, and should make possible precise measurements of black hole masses and spins. Indeed, the waves generated by such a capture will encode a detailed description of the black hole's spacetime, making it possible to test whether the ''large object'' in the galactic nucleus is indeed a Kerr black hole as predicted by general relativity, or is some exotic massive compact object ͓3,4͔.Extracting such information will require accurate modeling of the gravitational waveform. The smallness of the system's mass ratio ͑typically, /M ϳ10 Ϫ4 Ϫ10 Ϫ6 , where and M are the masses for the captured body and the central hole, respectively͒ allows one to treat the small body as a ''test particle'' moving in the gravitational field of the black hole. In the absence of radiation, the small body moves on a geodesic orbit of the black hole ͓5͔. These orbits have three integrals of motion ͑apart from ): energy E; angular momentum projected on the hole's spin axis, L z ; and Carter's third constant Q, related to the square of the angular momentum projected onto the equatorial plane. A body in a generic ͑eccentric and inclined͒ Kerr orbit traces an open ellipse precessing about the black hole's spin axis, resulting in a complicated overall motion. Astrophysical captured bodies will move in such complicated orbits.The integrals of the motion are not constant in the presence of gravitational radiation-they evolve as...

We study eccentric equatorial orbits of a test-body around a Kerr black hole under the influence of gravitational radiation reaction. We have adopted a well established two-step approach: assuming that the particle is moving along a geodesic ͑justifiable as long as the orbital evolution is adiabatic͒ we calculate numerically the fluxes of energy and angular momentum radiated to infinity and to the black hole horizon, via the TeukolskySasaki-Nakamura formalism. We can then infer the rate of change of orbital energy and angular momentum and thus the evolution of the orbit. The orbits are fully described by a semilatus rectum p and an eccentricity e. We find that while, during the inspiral, e decreases until shortly before the orbit reaches the separatrix of stable bound orbits ͓which is defined by p s (e)͔, in many astrophysically relevant cases the eccentricity will still be significant in the last stages of the inspiral. In addition, when a critical value p crit (e) is reached, the eccentricity begins to increase as a result of continued radiation induced inspiral. The two values p s , p crit ͑for given e) move closer to each other, in coordinate terms, as the black hole spin is increased, as they do also for fixed spin and increasing eccentricity. Of particular interest are moderate and high eccentricity orbits around rapidly spinning black holes, with p(e)Ϸp s (e). We call these ''zoom-whirl'' orbits, because of their characteristic behavior involving several revolutions around the central body near periastron. Gravitational waveforms produced by such orbits are calculated and shown to have a very particular signature. Such signals may well prove of considerable astrophysical importance for the future Laser Interferometer Space Antenna detector.