Bulletin of the American Physical Society
APS April Meeting 2010
Volume 55, Number 1
Saturday–Tuesday, February 13–16, 2010; Washington, DC
Session K14: Approximations in General Relativity |
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Sponsoring Units: GGR Chair: Steven Detweiler, University of Florida Room: Washington 4 |
Sunday, February 14, 2010 3:30PM - 3:42PM |
K14.00001: A solution to the Fouth order Killing Equations Jeandrew Brink I present a closed form analytic solution to the fourth order Killing equations in stationary axisymmetric vacuum spacetimes. Properties of the solution as well as implications for gravitational wave observations are discussed. [Preview Abstract] |
Sunday, February 14, 2010 3:42PM - 3:54PM |
K14.00002: Self-force with numerical relativity tools Ian Vega, Peter Diener, Wolfgang Tichy, Steve Detweiler We review recent progress towards developing an approach to self-force problems that take advantage of extant infrastructure within numerical relativity. We shall describe our prescription and its application to the case of a scalar charge in a circular orbit around a Schwarzschild black hole with the use of two evolution codes originally written for numerical relativity applications. Within this framework, the self-force on the charge and the corresponding energy fluxes are computed to within $1\%$ of the known correct answer. This constitutes the first successful calculation of a self-force in a (3+1) setting. [Preview Abstract] |
Sunday, February 14, 2010 3:54PM - 4:06PM |
K14.00003: Hamiltonian of a spinning test-particle in curved spacetime Enrico Barausse, Etienne Racine, Alessandra Buonanno Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test-particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase-space algebra in the Newton-Wigner spin supplementary condition (SSC), suitably generalized to curved spacetime, and find that the phase-space algebra $(\mathbf{q},\mathbf{p},\mathbf{S})$ is canonical at linear order in the particle spin. We provide explicit expressions for this Hamiltonian in a spherically symmetric spacetime, both in isotropic and spherical coordinates, and in the Kerr spacetime in Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when expanded in Post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner (ADM) canonical Hamiltonian computed in PN theory in the test-particle limit. Notably, we recover the known spin-orbit couplings through 2.5PN order and the spin-spin couplings of type $S_{\rm Kerr}\,S$ (and $S_{\rm Kerr}^2$) through 3PN order, $S_{\rm Kerr}$ being the spin of the Kerr spacetime. Our method allows one to compute the PN Hamiltonian at any order, in the test-particle limit and at linear order in the particle spin. As an application we compute it at 3.5PN order. [Preview Abstract] |
Sunday, February 14, 2010 4:06PM - 4:18PM |
K14.00004: Analysis of extreme mass ratio inspirals in Kerr: Transition from inspiral to plunge Tanja Hinderer The gravitational radiation reaction driven inspiral of a compact object into a much more massive Kerr black hole proceeds through three different regimes: (i) An adiabatic inspiral, where the inspiral time scale is much larger than the orbital period and which can be modeled theoretically using two-timescale expansions, (ii) a transition regime near the separatrix where the orbit becomes unstable, and (iii) the infall which can be approximated as a geodesic plunge. A systematic local analysis of the orbital dynamics near the separatrix together with matched asymptotic expansions shows that the effect of passing through the transition regime amounts to small shifts in the constants of motion, whose magnitudes can be computed, together with a time adjustment. These results give insight into how the information about the initial conditions from the beginning of the inspiral is passed through the separatrix to give the initial conditions for the plunge. Since the timescale for the plunge is much shorter than the radiation reaction timescale, the plunging orbit will closely track the corresponding unperturbed separatrix trajectory. A detailed theoretical model of the near-separatrix dynamics for generic orbits is important for understanding features such as zoom-whirl behavior. [Preview Abstract] |
Sunday, February 14, 2010 4:18PM - 4:30PM |
K14.00005: Geometry and dynamics of a tidally deformed black hole Eric Poisson The metric of a nonrotating black hole deformed by a tidal interaction is calculated and expressed as an expansion in the strength of the tidal coupling. The expansion parameter is the inverse length scale ${\cal R}^{-1}$, where $\cal R$ is the radius of curvature of the external spacetime in which the black hole moves. The expansion begins at order ${\cal R}^{-2}$, and it is carried out through order ${\cal R}^{-4}$. The metric is parameterized by a number of tidal multipole moments, which specify the black hole's tidal environment. The tidal moments are freely-specifiable functions of time that are related to the Weyl tensor of the external spacetime. The metric is presented in a light-cone coordinate system that possesses a clear geometrical meaning. At the order of accuracy maintained in this work, the horizon is a stationary null hypersurface foliated by apparent horizons; it is an isolated horizon in the sense of Ashtekar and Krishnan. As an application of our results we examine the induced geometry and dynamics of the horizon, and calculate the rate at which the black-hole surface area increases as a result of the tidal interaction. [Preview Abstract] |
Sunday, February 14, 2010 4:30PM - 4:42PM |
K14.00006: Accurate analytical waveforms of coalescing binary black holes Yi Pan I will present analytical waveforms of gravitational-wave radiation from coalescing binary black holes generated within the analytical effective-one-body approach. These waveforms agree, within numerical errors, with waveforms generated by highly accurate numerical relativity simulations. Furthermore, in the test-particle limit, these waveforms agree with the extreme mass ratio inspiral waveforms generated by numerically solving the Teukolsky equations. I will show how this analytical approach extracts non-perturbative information contained in the numerical simulations, models the full coalescence phase, and provides a sufficiently accurate bank of waveforms to be used in matched-filtering based searches of coalescing binary black holes with ground-based gravitational-wave detectors. [Preview Abstract] |
Sunday, February 14, 2010 4:42PM - 4:54PM |
K14.00007: Searching for a Carter-like constant of motion in the Bach-Weyl solution Saeed Mirshekari, Clifford Will It was recently shown [1] that the Newtonian gravitational field of two fixed point masses has multipole moments linked by the same relation as those for Kerr black holes, and that there is a Carter-like constant of the motion for this system. In this work, we study whether the general relativistic analogue, the Bach-Weyl solution, also has a Carter-like constant. We carry this out by (1) searching for a symmetric Killing tensor for the Bach-Weyl spacetime, and (2) trying to construct a Carter-like constant in its post-Newtonian limit. Preliminary results will be reported.\\[4pt] [1] C. M. Will, Phys. Rev. Lett. 102, 061101 (2009) [Preview Abstract] |
Sunday, February 14, 2010 4:54PM - 5:06PM |
K14.00008: A Hybrid Approximation Technique for Head-on Black-Hole-Binary Mergers David Nichols, Yanbei Chen, Drew Keppel, Geoffrey Lovelace, Ulrich Sperhake Black-hole-binary coalescence is often divided into three stages, inspiral, merger and ringdown; the post-Newtonian (PN) approximation treats the inspiral phase, black-hole perturbation (BHP) theory describes the ringdown, and the strongly nonlinear dynamics of spacetime characterize the merger. In this paper, we introduce a hybrid method that incorporates elements of PN and BHP theories, and we apply it to the head-on collision of black holes with transverse, anti-parallel spins. We compare our approximation technique with a full numerical-relativity simulation by G. Lovelace et al, and we find surprisingly good agreement between the gravitational waveforms and the radiated energy and momentum. We also apply this model to understand the flow of gravitational field momentum in the simulation, quantified by the Landau-Lifshitz pseudotensor. Our results indicate that while PN and BHP theories do not capture all the strongly nonlinear physics of the merger, they do suffice to explain the outgoing gravitational radiation for head-on mergers. [Preview Abstract] |
Sunday, February 14, 2010 5:06PM - 5:18PM |
K14.00009: Gravitational self-force meets the post-Newtonian approximation in extreme-mass ratio inspiral of binary black holes Steven Detweiler Post-Newtonian analysis, numerical relativity and, now, perturbation-based gravitational self-force analysis are all being used to describe various aspects of black hole binary systems. Recent comparisons between self-force analysis, with $m_1\ll m_2$, and post-Newtonian analysis, with $v/c \ll 1$ show excellent agreement in their common domain of validity. This lends credence to the two very different regularization procedures which are invoked in these approximations. When self-force analysis is able to create gravitational waveforms from extreme mass-ratio inspiral, then unprecedented cross cultural comparisons of these three distinct approaches to understanding gravitational waves will reveal the strengths and weaknesses of each. [Preview Abstract] |
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