M. Favata

Consequences of Gravitational Radiation Recoil

Coalescing binary black holes experience an impulsive kick due to anisotropic emission of gravitational waves. We discuss the dynamical consequences of the recoil accompanying massive black hole mergers. Recoil velocities are sufficient to eject most coalescing black holes from dwarf galaxies and globular clusters, which may explain the apparent absence of massive black holes in these systems. Ejection from giant elliptical galaxies would be rare, but coalescing black holes are displaced from the center and fall back on a time scale of order the half-mass crossing time. Displacement of the black holes transfers energy to the stars in the nucleus and can convert a steep density cusp into a core. Radiation recoil calls into question models that grow supermassive black holes from hierarchical mergers of stellar-mass precursors. Subject headings: black hole physics — gravitation — gravitational waves — galaxies: nuclei

The transient gravitational-wave sky

Interferometric detectors will very soon give us an unprecedented view of the gravitational-wave sky, and in particular of the explosive and transient Universe. Now is the time to challenge our theoretical understanding of short-duration gravitational-wave signatures from cataclysmic events, their connection to more traditional electromagnetic and particle astrophysics, and the data analysis techniques that will make the observations a reality. This paper summarizes the state of the art, future science opportunities, and current challenges in understanding gravitational-wave transients.

The gravitational-wave memory effect

The nonlinear memory effect is a slowly growing, non-oscillatory contribution to the gravitational-wave amplitude. It originates from gravitational waves that are sourced by the previously emitted waves. In an ideal gravitational-wave interferometer a gravitational wave with memory causes a permanent displacement of the test masses that persists after the wave has passed. Surprisingly, the nonlinear memory affects the signal amplitude starting at leading (Newtonian-quadrupole) order. Despite this fact, the nonlinear memory is not easily extracted from current numerical relativity simulations. After reviewing the linear and nonlinear memory I summarize some recent work, including (1) computations of the memory contribution to the inspiral waveform amplitude (thus completing the waveform to third post-Newtonian order); (2) the first calculations of the nonlinear memory that include all phases of binary black hole coalescence (inspiral, merger, ringdown); and (3) realistic estimates of the detectability of the memory with LISA.

Nonlinear Gravitational-Wave Memory from Binary Black Hole Mergers

Some astrophysical sources of gravitational waves can produce a memory effect, which causes a permanent displacement of the test masses in a freely falling gravitational-wave detector. The Christodoulou memory is a particularly interesting nonlinear form of memory that arises from the gravitational-wave stress-energy tensors contribution to the distant gravitational-wave field. This nonlinear memory contributes a nonoscillatory component to the gravitational-wave signal at leading (Newtonian-quadrupole) order in the waveform amplitude. Previous computations of the memory and its detectability considered only the inspiral phase of binary black hole coalescence. Using an effective-one-body (EOB) approach calibrated to numerical relativity simulations, as well as a simple fully analytic model, the Christodoulou memory is computed for the inspiral, merger, and ringdown. The memory will be very difficult to detect with ground-based interferometers, but is likely to be observable in supermassive black hole mergers with LISA out to redshifts z 2. Detection of the nonlinear memory could serve as an experimental test of the ability of gravity to gravitate.

Energy localization invariance of tidal work in general relativity

It is well known that when an external general relativistic (electric-type) tidal field Ejk(t) interacts with the evolving quadrupole moment Ijk(t) of an isolated body the tidal field does work on the body (“tidal work”)—i.e., it transfers energy to the body—at a rate given by the same formula as in Newtonian theory: dW/dt=-1/2EjkdIjk/dt. Thorne has posed the following question: In view of the fact that the gravitational interaction energy Eint between the tidal field and the body is ambiguous by an amount ∼EjkIjk, is the tidal work also ambiguous by this amount, and therefore is the formula dW/dt=-1/2EjkdIjk/dt only valid unambiguously when integrated over time scales long compared to that for Ijk to change substantially? This paper completes a demonstration that the answer is no; dW/dt is not ambiguous in this way. More specifically, this paper shows that dW/dt is unambiguously given by -1/2EjkdIjk/dt independently of one’s choice of how to localize gravitational energy in general relativity. This is proved by explicitly computing dW/dt using various gravitational stress-energy pseudotensors (Einstein, Landau-Lifshitz, Moller) as well as Bergmann’s conserved quantities which generalize many of the pseudotensors to include an arbitrary function of position. A discussion is also given of the problem of formulating conservation laws in general relativity and the role played by the various pseudotensors.

Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: A New gauge-invariant post-Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force

The innermost stable circular orbit (ISCO) delimits the transition from circular orbits to those that plunge into a black hole. In the test-mass limit, well-defined ISCO conditions exist for the Kerr and Schwarzschild spacetimes. In the finite-mass case, there are a large variety of ways to define an ISCO in a post-Newtonian (PN) context. Here I generalize the gauge-invariant ISCO condition of Blanchet and Iyer [Classical Quantum Gravity 20, 755 (2003)] to the case of spinning (nonprecessing) binaries. The Blanchet-Iyer ISCO condition has two desirable and unexpected properties: (1) it exactly reproduces the Schwarzschild ISCO in the test-mass limit, and (2) it accurately approximates the recently calculated shift in the Schwarzschild ISCO frequency due to the conservative-piece of the gravitational self-force [L. Barack and N. Sago, Phys. Rev. Lett. 102, 191101 (2009)]. The generalization of this ISCO condition to spinning binaries has the property that it also exactly reproduces the Kerr ISCO in the test-mass limit (up to the order at which PN spin corrections are currently known). The shift in the ISCO due to the spin of the test-particle is also calculated. Remarkably, the gauge-invariant PN ISCO condition exactly reproduces the ISCO shift predicted by the Papapetrou equations for a fully relativistic spinning particle. It is surprising that an analysis of the stability of the standard PN equations of motion is able (without any form of “resummation”) to accurately describe strong-field effects of the Kerr spacetime. The ISCO frequency shift due to the conservative self-force in Kerr is also calculated from this new ISCO condition, as well as from the effective-one-body Hamiltonian of Barausse and Buonanno [Phys. Rev. D 81, 084024 (2010)]. These results serve as a useful point of comparison for future gravitational self-force calculations in the Kerr spacetime.

The Gravitational-wave memory from eccentric binaries

The nonlinear gravitational-wave memory causes a time-varying but nonoscillatory correction to the gravitational-wave polarizations. It arises from gravitational-waves that are sourced by gravitational-waves. Previous considerations of the nonlinear memory effect have focused on quasicircular binaries. Here I consider the nonlinear memory from Newtonian orbits with arbitrary eccentricity. Expressions for the waveform polarizations and spin-weighted spherical-harmonic modes are derived for elliptic, hyperbolic, parabolic, and radial orbits. In the hyperbolic, parabolic, and radial cases the nonlinear memory provides a 2.5 post-Newtonian (PN) correction to the leading-order waveforms. This is in contrast to the elliptical and quasicircular cases, where the nonlinear memory corrects the waveform at leading (0PN) order. This difference in PN order arises from the fact that the memory builds up over a short “scattering” time scale in the hyperbolic case, as opposed to a much longer radiation-reaction time scale in the elliptical case. The nonlinear memory corrections presented here complete our knowledge of the leading-order (Peters-Mathews) waveforms for elliptical orbits. These calculations are also relevant for binaries with quasicircular orbits in the present epoch which had, in the past, large eccentricities. Because the nonlinear memory depends sensitively on the past evolution of a binary, I discuss the effect of this early-time eccentricity on the value of the late-time memory in nearly circularized binaries. I also discuss the observability of large “memory jumps” in a binary’s past that could arise from its formation in a capture process. Lastly, I provide estimates of the signal-to-noise ratio of the linear and nonlinear memories from hyperbolic and parabolic binaries.

Summary of session B3: analytic 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, 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.