Asymptotically Matched Spacetime Metric for Non-Precessing, Spinning Black Hole Binaries

We construct a closed-form, fully analytical 4-metric that approximately represents the spacetime evolution of non-precessing, spinning black hole binaries from infinite separations up to a few orbits prior to merger. We employ the technique of asymptotic matching to join a perturbed Kerr metric in the neighborhood of each spinning black hole to a near-zone, post-Newtonian metric farther out. The latter is already naturally matched to a far-zone, post-Minkowskian metric that accounts for full temporal retardation. The result is a 4-metric that is approximately valid everywhere in space and in a small bundle of spatial hypersurfaces. We here restrict our attention to quasi- circular orbits, but the method is valid for any orbital motion or physical scenario, provided an overlapping region of validity or buffer zone exists. A simple extension of such a metric will allow for future studies of the accretion disk and jet dynamics around spinning back hole binaries

Complete adiabatic waveform templates for a test-mass in the Schwarzschild spacetime: VIRGO and Advanced LIGO studies

Post-Newtonian expansions of the binding energy and gravitational wave flux truncated at the {\it same relative} post-Newtonian order form the basis of the {\it standard adiabatic} approximation to the phasing of gravitational waves from inspiralling compact binaries. Viewed in terms of the dynamics of the binary, the standard approximation is equivalent to neglecting certain conservative post-Newtonian terms in the acceleration. In an earlier work, we had proposed a new {\it complete adiabatic} approximant constructed from the energy and flux functions. At the leading order it employs the 2PN energy function rather than the 0PN one in the standard approximation, so that, effectively the approximation corresponds to the dynamics where there are no missing post-Newtonian terms in the acceleration. In this paper, we compare the overlaps of the standard and complete adiabatic templates with the exact waveform in the adiabatic approximation of a test-mass motion in the Schwarzschild spacetime, for the VIRGO and the Advanced LIGO noise spectra. It is found that the complete adiabatic approximants lead to a remarkable improvement in the {\it effectualness} at lower PN ($<$ 3PN) orders, while standard approximants of order $\geq$ 3PN provide a good lower-bound to the complete approximants for the construction of effectual templates. {\it Faithfulness} of complete approximants is better than that of standard approximants except for a few post-Newtonian orders. Standard and complete approximants beyond the adiabatic approximation are also studied using the Lagrangian templates of Buonanno, Chen and Vallisneri.Comment: Proceedings of the GWDAW-9, Accepted for publication in Class. Quant. Gra

Matching post-Newtonian and numerical relativity waveforms: systematic errors and a new phenomenological model for non-precessing black hole binaries

We present a new phenomenological gravitational waveform model for the inspiral and coalescence of non-precessing spinning black hole binaries. Our approach is based on a frequency domain matching of post-Newtonian inspiral waveforms with numerical relativity based binary black hole coalescence waveforms. We quantify the various possible sources of systematic errors that arise in matching post-Newtonian and numerical relativity waveforms, and we use a matching criteria based on minimizing these errors; we find that the dominant source of errors are those in the post-Newtonian waveforms near the merger. An analytical formula for the dominant mode of the gravitational radiation of non-precessing black hole binaries is presented that captures the phenomenology of the hybrid waveforms. Its implementation in the current searches for gravitational waves should allow cross-checks of other inspiral-merger-ringdown waveform families and improve the reach of gravitational wave searches.Comment: 22 pages, 11 figure

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

Dual Linearised Gravity in Arbitrary Dimensions

We construct dual formulation of linearised gravity in first order tetrad formalism in arbitrary dimensions within the path integral framework following the standard duality algorithm making use of the global shift symmetry of the tetrad field. The dual partition function is in terms of the (mixed symmetric) tensor field $\Phi_{[\nu_{1}\nu_{2}...\nu_{d-3}]\nu}$ in {\it frame-like} formulation. We obtain in d-dimensions the dual Lagrangian in a closed form in terms of field strength of the dual frame-like field. Next by coupling a source with the (linear) Riemann tensor in d-dimensions, dual generating functional is obtained. Using this an operator mapping between (linear) Riemann tensor and Riemann tensor corresponding to the dual field is derived and we also discuss the exchange of equations of motion and Bianchi identity.Comment: 14 pages, typos corrected, Published version: Class. Quantum Grav. 22(2005)538

Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity

The accurate modeling of gravitational radiation is a key issue for gravitational wave astronomy. As simulation codes reach higher accuracy, systematic errors inherent in current numerical relativity wave-extraction methods become evident, and may lead to a wrong astrophysical interpretation of the data. In this paper, we give a detailed description of the Cauchy-characteristic extraction technique applied to binary black hole inspiral and merger evolutions to obtain gravitational waveforms that are defined unambiguously, that is, at future null infinity. By this method we remove finite-radius approximations and the need to extrapolate data from the near zone. Further, we demonstrate that the method is free of gauge effects and thus is affected only by numerical error. Various consistency checks reveal that energy and angular momentum are conserved to high precision and agree very well with extrapolated data. In addition, we revisit the computation of the gravitational recoil and find that finite radius extrapolation very well approximates the result at \scri. However, the (non-convergent) systematic differences to extrapolated data are of the same order of magnitude as the (convergent) discretisation error of the Cauchy evolution hence highlighting the need for correct wave-extraction.Comment: 41 pages, 8 figures, 2 tables, added references, fixed typos. Version matches published version