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

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

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

The physical hamiltonian in nonperturbative quantum gravity

A quantum hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop representation, and is shown to be finite and diffeomorphism invariant. The problem of constructing this hamiltonian is reduced to a combinatorial and algebraic problem which involves the rearrangements of lines through the vertices of arbitrary graphs. This procedure also provides a construction of the hamiltonian constraint as a finite operator on the space of diffeomorphism invariant states as well as a construction of the operator corresponding to the spatial volume of the universe.Comment: Latex, 11 pages, no figures, CGPG/93/

Spin Networks and Quantum Gravity

We introduce a new basis on the state space of non-perturbative quantum gravity. The states of this basis are linearly independent, are well defined in both the loop representation and the connection representation, and are labeled by a generalization of Penrose's spin netoworks. The new basis fully reduces the spinor identities (SU(2) Mandelstam identities) and simplifies calculations in non-perturbative quantum gravity. In particular, it allows a simple expression for the exact solutions of the Hamiltonian constraint (Wheeler-DeWitt equation) that have been discovered in the loop representation. Since the states in this basis diagnolize operators that represent the three geometry of space, such as the area and volumes of arbitrary surfaces and regions, these states provide a discrete picture of quantum geometry at the Planck scale.Comment: 42 page

Comparisons of binary black hole merger waveforms

This a particularly exciting time for gravitational wave physics. Ground-based gravitational wave detectors are now operating at a sensitivity such that gravitational radiation may soon be directly detected, and recently several groups have independently made significant breakthroughs that have finally enabled numerical relativists to solve the Einstein field equations for coalescing black-hole binaries, a key source of gravitational radiation. The numerical relativity community is now in the position to begin providing simulated merger waveforms for use by the data analysis community, and it is therefore very important that we provide ways to validate the results produced by various numerical approaches. Here, we present a simple comparison of the waveforms produced by two very different, but equally successful approaches--the generalized harmonic gauge and the moving puncture methods. We compare waveforms of equal-mass black hole mergers with minimal or vanishing spins. The results show exceptional agreement for the final burst of radiation, with some differences attributable to small spins on the black holes in one case.Comment: Revtex 4, 5 pages. Published versio

Generic Tracking of Multiple Apparent Horizons with Level Flow

We report the development of the first apparent horizon locator capable of finding multiple apparent horizons in a ``generic'' numerical black hole spacetime. We use a level-flow method which, starting from a single arbitrary initial trial surface, can undergo topology changes as it flows towards disjoint apparent horizons if they are present. The level flow method has two advantages: 1) The solution is independent of changes in the initial guess and 2) The solution can have multiple components. We illustrate our method of locating apparent horizons by tracking horizon components in a short Kerr-Schild binary black hole grazing collision.Comment: 13 pages including figures, submitted to Phys Rev