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We study the transition from inspiral to plunge in general relativity bycomputing gravitational waveforms of non-spinning, equal-mass black-holebinaries. We consider three sequences of simulations, starting with aquasi-circular inspiral completing 1.5, 2.3 and 9.6 orbits, respectively, priorto coalescence of the holes. For each sequence, the binding energy of thesystem is kept constant and the orbital angular momentum is progressivelyreduced, producing orbits of increasing eccentricity and eventually a head-oncollision. We analyze in detail the radiation of energy and angular momentum ingravitational waves, the contribution of different multipolar components andthe final spin of the remnant. We find that the motion transitions frominspiral to plunge when the orbital angular momentum L=L_crit is about 0.8M^2.For L<L_crit the radiated energy drops very rapidly. Orbits with L of aboutL_crit produce our largest dimensionless Kerr parameter for the remnant,j=J/M^2=0.724. Generalizing a model recently proposed by Buonanno, Kidder andLehner to eccentric binaries, we conjecture that (1) j=0.724 is the maximalKerr parameter that can be obtained by any merger of non-spinning holes, and(2) no binary merger (even if the binary members are extremal Kerr black holeswith spins aligned to the orbital angular momentum, and the inspiral is highlyeccentric) can violate the cosmic censorship conjecture.

Eccentric binary black-hole mergers: The transition from inspiral to plunge in general relativity