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 non-spinning, equal-mass black-hole binaries. We consider three sequences of simulations, starting with a quasi-circular 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. We find that the motion transitions from inspiral 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 about L_crit produce our largest dimensionless Kerr parameter for the remnant, j=J/M^2=0.724. Generalizing a model recently proposed by Buonanno, Kidder and Lehner to eccentric binaries, we conjecture that (1) j=0.724 is the maximal Kerr 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 holes with spins aligned to the orbital angular momentum, and the inspiral is highly eccentric) can violate the cosmic censorship conjecture.Comment: Added sequence of long inspirals to the study. To match published versio

Late Time Analysis for Maximal Slicing of Reissner-Nordström Puncture Evolutions

We perform an analytic late time analysis for maximal slicing of the Reissner-Nordstr\"om black hole spacetime. In particular, we discuss the collapse of the lapse in terms of its late time behavior at the throat and at the event horizon for the even and the puncture lapse. In the latter case we also determine the value of the lapse at the puncture. Furthermore, in the limit of late times slice stretching effects are studied as they arise for maximal slicing of puncture evolutions. We perform numerical experiments for a Schwarzschild black hole with puncture lapse and find agreement with the analytical results

Investigating the mass-ratio dependence of the prompt-collapse threshold with numerical-relativity simulations

The next observing runs of advanced gravitational-wave detectors will lead to a variety of binary neutron star detections and numerous possibilities for multi-messenger observations of binary neutron star systems. In this context a clear understanding of the merger process and the possibility of prompt black hole formation after merger is important, as the amount of ejected material strongly depends on the merger dynamics. These dynamics are primarily affected by the total mass of the binary, however, the mass ratio also influences the postmerger evolution. To determine the effect of the mass ratio, we investigate the parameter space around the prompt-collapse threshold with a new set of fully relativistic simulations. The simulations cover three equations of state and seven mass ratios in the range of $1.0 \leq q \leq 1.75$, with five to seven simulations of binary systems of different total mass in each case. The threshold mass is determined through an empirical relation based on the collapse-time, which allows us to investigate effects of the mass-ratio on the threshold mass and also on the properties of the remnant system. Furthermore, we model effects of mass ratio and equation of state on tidal parameters of threshold configurations

Ill-posedness in the Einstein equations

It is shown that the formulation of the Einstein equations widely in use in numerical relativity, namely, the standard ADM form, as well as some of its variations (including the most recent conformally-decomposed version), suffers from a certain but standard type of ill-posedness. Specifically, the norm of the solution is not bounded by the norm of the initial data irrespective of the data. A long-running numerical experiment is performed as well, showing that the type of ill-posedness observed may not be serious in specific practical applications, as is known from many numerical simulations.Comment: 13 pages, 3 figures, accepted for publication in Journal of Mathematical Physics (to appear August 2000

High-accuracy simulations of highly spinning binary neutron star systems

With an increasing number of expected gravitational-wave detections of binary neutron star mergers, it is essential that gravitational-wave models employed for the analysis of observational data are able to describe generic compact binary systems. This includes systems in which the individual neutron stars are millisecond pulsars for which spin effects become essential. In this work, we perform numerical-relativity simulations of binary neutron stars with aligned and anti-aligned spins within a range of dimensionless spins of $\chi \sim [-0.28,0.58]$. The simulations are performed with multiple resolutions, show a clear convergence order and, consequently, can be used to test existing waveform approximants. We find that for very high spins gravitational-wave models that have been employed for the interpretation of GW170817 and GW190425 are not capable of describing our numerical-relativity dataset. We verify through a full parameter estimation study in which clear biases in the estimate of the tidal deformability and effective spin are present. We hope that in preparation of the next gravitational-wave observing run of the Advanced LIGO and Advanced Virgo detectors our new set of numerical-relativity data can be used to support future developments of new gravitational-wave models

Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins

We present the first analytical inspiral-merger-ringdown gravitational waveforms from binary black holes (BBHs) with non-precessing spins, that is based on a description of the late-inspiral, merger and ringdown in full general relativity. By matching a post-Newtonian description of the inspiral to a set of numerical-relativity simulations, we obtain a waveform family with a conveniently small number of physical parameters. These waveforms will allow us to detect a larger parameter space of BBH coalescence, including a considerable fraction of precessing binaries in the comparable-mass regime, thus significantly improving the expected detection rates.Comment: To appear in Phys. Rev. Lett. Significant new results. One figure removed due to page limitatio

Covariant quantization of membrane dynamics

A Lorentz covariant quantization of membrane dynamics is defined, which also leaves unbroken the full three dimensional diffeomorphism invariance of the membrane. Among the applications studied are the reduction to string theory, which may be understood in terms of the phase space and constraints, and the interpretation of physical,zero-energy states. A matrix regularization is defined as in the light cone gauged fixed theory but there are difficulties implementing all the gauge symmetries. The problem involves the non-area-preserving diffeomorphisms which are realized non-linearly in the classical theory. In the quantum theory they do not seem to have a consistent implementation for finite N. Finally, an approach to a genuinely background independent formulation of matrix dynamics is briefly described.Comment: Latex, 21 pages, no figure

Finite, diffeomorphism invariant observables in quantum gravity

Two sets of spatially diffeomorphism invariant operators are constructed in the loop representation formulation of quantum gravity. This is done by coupling general relativity to an anti- symmetric tensor gauge field and using that field to pick out sets of surfaces, with boundaries, in the spatial three manifold. The two sets of observables then measure the areas of these surfaces and the Wilson loops for the self-dual connection around their boundaries. The operators that represent these observables are finite and background independent when constructed through a proper regularization procedure. Furthermore, the spectra of the area operators are discrete so that the possible values that one can obtain by a measurement of the area of a physical surface in quantum gravity are valued in a discrete set that includes integral multiples of half the Planck area. These results make possible the construction of a correspondence between any three geometry whose curvature is small in Planck units and a diffeomorphism invariant state of the gravitational and matter fields. This correspondence relies on the approximation of the classical geometry by a piecewise flat Regge manifold, which is then put in correspondence with a diffeomorphism invariant state of the gravity-matter system in which the matter fields specify the faces of the triangulation and the gravitational field is in an eigenstate of the operators that measure their areas.Comment: Latex, no figures, 30 pages, SU-GP-93/1-

Regularization of the Hamiltonian constraint and the closure of the constraint algebra

In the paper we discuss the process of regularization of the Hamiltonian constraint in the Ashtekar approach to quantizing gravity. We show in detail the calculation of the action of the regulated Hamiltonian constraint on Wilson loops. An important issue considered in the paper is the closure of the constraint algebra. The main result we obtain is that the Poisson bracket between the regulated Hamiltonian constraint and the Diffeomorphism constraint is equal to a sum of regulated Hamiltonian constraints with appropriately redefined regulating functions.Comment: 23 pages, epsfig.st