Gravitational-Wave Recoil from the Ringdown Phase of Coalescing Black Hole Binaries

The gravitational recoil or "kick" of a black hole formed from the merger of two orbiting black holes, and caused by the anisotropic emission of gravitational radiation, is an astrophysically important phenomenon. We combine (i) an earlier calculation, using post-Newtonian theory, of the kick velocity accumulated up to the merger of two non-spinning black holes, (ii) a "close-limit approximation" calculation of the radiation emitted during the ringdown phase, and based on a solution of the Regge-Wheeler and Zerilli equations using initial data accurate to second post-Newtonian order. We prove that ringdown radiation produces a significant "anti-kick". Adding the contributions due to inspiral, merger and ringdown phases, our results for the net kick velocity agree with those from numerical relativity to 10-15 percent over a wide range of mass ratios, with a maximum velocity of 180 km/s at a mass ratio of 0.38.Comment: 9 pages, 5 figures; to appear in Class. Quant. Gra

Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems

Using the first law of binary black-hole mechanics, we compute the binding energy E and total angular momentum J of two non-spinning compact objects moving on circular orbits with frequency Omega, at leading order beyond the test-particle approximation. By minimizing E(Omega) we recover the exact frequency shift of the Schwarzschild innermost stable circular orbit induced by the conservative piece of the gravitational self-force. Comparing our results for the coordinate invariant relation E(J) to those recently obtained from numerical simulations of comparable-mass non-spinning black-hole binaries, we find a remarkably good agreement, even in the strong-field regime. Our findings confirm that the domain of validity of perturbative calculations may extend well beyond the extreme mass-ratio limit.Comment: 5 pages, 1 figure; matches the published versio

Spacetime Symmetries and Kepler's Third Law

The curved spacetime geometry of a system of two point masses moving on a circular orbit has a helical symmetry. We show how Kepler's third law for circular motion, and its generalization in post-Newtonian theory, can be recovered from a simple, covariant condition on the norm of the associated helical Killing vector field. This unusual derivation can be used to illustrate some concepts of prime importance in a general relativity course, including those of Killing field, covariance, coordinate dependence, and gravitational redshift.Comment: 11 pages, 3 figures; minor changes and text improvements; matches version to appear in Class. Quant. Gra

Modeling Gravitational Recoil Using Numerical Relativity

We review the developments in modeling gravitational recoil from merging black-hole binaries and introduce a new set of 20 simulations to test our previously proposed empirical formula for the recoil. The configurations are chosen to represent generic binaries with unequal masses and precessing spins. Results of these simulations indicate that the recoil formula is accurate to within a few km/s in the similar mass-ratio regime for the out-of-plane recoil.Comment: corrections to text, 11 pages, 1 figur

Model of Dark Matter and Dark Energy Based on Gravitational Polarization

A model of dark matter and dark energy based on the concept of gravitational polarization is investigated. We propose an action in standard general relativity for describing, at some effective or phenomenological level, the dynamics of a dipolar medium, i.e. one endowed with a dipole moment vector, and polarizable in a gravitational field. Using first-order cosmological perturbations, we show that the dipolar fluid is undistinguishable from standard dark energy (a cosmological constant Lambda) plus standard dark matter (a pressureless perfect fluid), and therefore benefits from the successes of the Lambda-CDM (Lambda-cold dark matter) scenario at cosmological scales. Invoking an argument of "weak clusterisation" of the mass distribution of dipole moments, we find that the dipolar dark matter reproduces the phenomenology of the modified Newtonian dynamics (MOND) at galactic scales. The dipolar medium action naturally contains a cosmological constant, and we show that if the model is to come from some fundamental underlying physics, the cosmological constant Lambda should be of the order of a0^2/c^4, where a0 denotes the MOND constant acceleration scale, in good agreement with observations.Comment: 38 pages, 4 figures; to appear in Phys. Rev.

Exploring new physics frontiers through numerical relativity

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology

Black holes, gravitational waves and fundamental physics: a roadmap

The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on 'Black holes, Gravitational waves and Fundamental Physics'