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

We study the transition from inspiral to plunge in general relativity by computing gravitational waveforms of nonspinning, equal- mass black- hole binaries. We consider three sequences of simulations, starting with a quasicircular inspiral completing 1.5, 2.3 and 9.6 orbits, respectively, prior to coalescence of the holes. For each sequence, the binding energy of the system is kept constant and the orbital angular momentum is progressively reduced, producing orbits of increasing eccentricity and eventually a head- on collision. We analyze in detail the radiation of energy and angular momentum in gravitational waves, the contribution of different multipolar components and the final spin of the remnant, comparing numerical predictions with the post- Newtonian approximation and with extrapolations of point- particle results. We find that the motion transitions from inspiral to plunge when the orbital angular momentum L = L-crit similar or equal to 0: 8M(2). For L< L-crit the radiated energy drops very rapidly. Orbits with L similar or equal to L-crit produce our largest dimensionless Kerr parameter for the remnant, j = J/M-2 similar or equal to 0.724 +/- 0.13 (to be compared with the Kerr parameter j similar or equal to 0.69 resulting from quasicircular inspirals). This value is in good agreement with the value of 0.72 reported in [I. Hinder, B. Vaishnav, F. Herrmann, D. Shoemaker, and P. Laguna, Phys. Rev. D 77, 081502 (2008).]. These conclusions are quite insensitive to the initial separation of the holes, and they can be understood by extrapolating point- particle results. Generalizing a model recently proposed by Buonanno, Kidder and Lehner [A. Buonanno, L. E. Kidder, and L. Lehner, Phys. Rev. D 77, 026004 (2008).] to eccentric binaries, we conjecture that (1) j similar or equal to 0.724 is close to the maximal Kerr parameter that can be obtained by any merger of nonspinning holes, and (2) no binary merger (even if the binary members are extremal Kerr black holes with spins aligned to the orbital angular momentum, and the inspiral is highly eccentric) can violate the cosmic censorship conjecture.