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We study eccentric equatorial orbits of a test-body around a Kerr black holeunder the influence of gravitational radiation reaction. We have adopted a wellestablished two-step approach: assuming that the particle is moving along ageodesic (justifiable as long as the orbital evolution is adiabatic) wecalculate numerically the fluxes of energy and angular momentum radiated toinfinity and to the black hole horizon, via the Teukolsky-Sasaki-Nakamuraformalism. We can then infer the rate of change of orbital energy and angularmomentum and thus the evolution of the orbit. The orbits are fully described bya semi-latus rectum $p$ and an eccentricity $e$. We find that while, during theinspiral, $e$ decreases until shortly before the orbit reaches the separatrixof stable bound orbits (which is defined by $p_{s}(e)$), in manyastrophysically relevant cases the eccentricity will still be significant inthe last stages of the inspiral. In addition, when a critical value$p_{crit}(e)$ is reached, the eccentricity begins to increase as a result ofcontinued radiation induced inspiral. The two values $p_{s}$, $p_{crit}$ (forgiven $e$) move closer to each other, in coordinate terms, as the black holespin is increased, as they do also for fixed spin and increasing eccentricity.Of particular interest are moderate and high eccentricity orbits around rapidlyspinning black holes, with $p(e) \approx p_{s}(e)$. We call these``zoom-whirl'' orbits, because of their characteristic behaviour involvingseveral revolutions around the central body near periastron. Gravitationalwaveforms produced by such orbits are calculated and shown to have a veryparticular signature. Such signals may well prove of considerable astrophysicalimportance for the future LISA detector.Comment: RevteX, 47 pages, 16 figures, submitted to Phys. Rev.

Zoom and whirl: Eccentric equatorial orbits around spinning black holes and their evolution under gravitational radiation reaction