Gravitational Recoil of Inspiralling Black-Hole Binaries to Second Post-Newtonian Order

The loss of linear momentum by gravitational radiation and the resulting gravitational recoil of black-hole binary systems may play an important role in the growth of massive black holes in early galaxies. We calculate the gravitational recoil of non-spinning black-hole binaries at the second post-Newtonian order (2PN) beyond the dominant effect, obtaining, for the first time, the 1.5PN correction term due to tails of waves and the next 2PN term. We find that the maximum value of the net recoil experienced by the binary due to the inspiral phase up to the innermost stable circular orbit (ISCO) is of the order of 22 km/s. We then estimate the kick velocity accumulated during the plunge from the ISCO up to the horizon by integrating the momentum flux using the 2PN formula along a plunge geodesic of the Schwarzschild metric. We find that the contribution of the plunge dominates over that of the inspiral. For a mass ratio m_2/m_1=1/8, we estimate a total recoil velocity (due to both adiabatic and plunge phases) of 100 +/- 20 km/s. For a ratio 0.38, the recoil is maximum and we estimate it to be 250 +/- 50 km/s. In the limit of small mass ratio, we estimate V/c to be approximately 0.043 (1 +/- 20%)(m_2/m_1)^2. Our estimates are consistent with, but span a substantially narrower range than, those of Favata et al. (2004).Comment: 19 pages, 1 figure, version accepted for publication in The Astrophysical Journa

Probing the non-linear structure of general relativity with black hole binaries

Observations of the inspiral of massive binary black holes (BBH) in the Laser Interferometer Space Antenna (LISA) and stellar mass binary black holes in the European Gravitational-Wave Observatory (EGO) offer an unique opportunity to test the non-linear structure of general relativity. For a binary composed of two non-spinning black holes, the non-linear general relativistic effects depend only on the masses of the constituents. In a recent letter, we explored the possibility of a test to determine all the post-Newtonian coefficients in the gravitational wave-phasing. However, mutual covariances dilute the effectiveness of such a test. In this paper, we propose a more powerful test in which the various post-Newtonian coefficients in the gravitational wave phasing are systematically measured by treating three of them as independent parameters and demanding their mutual consistency. LISA (EGO) will observe BBH inspirals with a signal-to-noise ratio of more than 1000 (100) and thereby test the self-consistency of each of the nine post-Newtonian coefficients that have so-far been computed, by measuring the lower order coefficients to a relative accuracy of $\sim 10^{-5}$ (respectively, $\sim 10^{-4}$) and the higher order coefficients to a relative accuracy in the range $10^{-4}$-0.1 (respectively, $10^{-3}$-1).Comment: 5 pages, 4 figures. Revised version, accepted for publication in Phys. Rev

Testing post-Newtonian theory with gravitational wave observations

The Laser Interferometric Space Antenna (LISA) will observe supermassive black hole binary mergers with amplitude signal-to-noise ratio of several thousands. We investigate the extent to which such observations afford high-precision tests of Einstein's gravity. We show that LISA provides a unique opportunity to probe the non-linear structure of post-Newtonian theory both in the context of general relativity and its alternatives.Comment: 9 pages, 2 figure

Inspiralling compact binaries in quasi-elliptical orbits: The complete third post-Newtonian energy flux

The instantaneous contributions to the 3PN gravitational wave luminosity from the inspiral phase of a binary system of compact objects moving in a quasi elliptical orbit is computed using the multipolar post-Minkowskian wave generation formalism. The necessary inputs for this calculation include the 3PN accurate mass quadrupole moment for general orbits and the mass octupole and current quadrupole moments at 2PN. Using the recently obtained 3PN quasi-Keplerian representation of elliptical orbits the flux is averaged over the binary's orbit. Supplementing this by the important hereditary contributions arising from tails, tails-of-tails and tails squared terms calculated in a previous paper, the complete 3PN energy flux is obtained. The final result presented in this paper would be needed for the construction of ready-to-use templates for binaries moving on non-circular orbits, a plausible class of sources not only for the space based detectors like LISA but also for the ground based ones.Comment: 40 pages. Minor changes in text throughout. Minor typos in Eqs. (3.3b), (7.7f), (8.19d) and (8.20) corrected. Matches the published versio

Analytic approximations, perturbation methods, and their applications

The paper summarizes the parallel session B3 {\em Analytic approximations, perturbation methods, and their applications} of the GR18 conference. The talks in the session reported notably recent advances in black hole perturbations and post-Newtonian approximations as applied to sources of gravitational waves.Comment: Summary of the B3 parallel session of the GR18 conferenc

Summary of Session B3Analytic Approximations, Perturbation Methods and Their Applications

The paper summarizes the parallel session B3 analytic approximations, perturbation methods and their applications of the GR18 conference. The talks in the session reported notably recent advances in black hole perturbations and post-Newtonian approximations as applied to sources of gravitational waves

Analytic approximations and perturbation methodsand their applications

The paper summarizes the parallel session B3 analytic approximations, perturbation methods and their applications of the GR18 conference. The talks in the session reported notably recent advances in black hole perturbations and post-Newtonian approximations as applied to sources of gravitational waves