19th Capra Meeting on Radiation Reaction in General Relativity

Babak

Alexandre Le Tiec — 2016-06-24T16:17:36Z

Speaker : S. Babak

Title : Results from O1 aLIGO run and impact on eLISA science

Abstract : In this review talk I will go through detection of two gravitational wave signals from binary black holes with LIGO detectors. I will describe the search, statistical significance evaluation and estimation of parameters of each binary system. Then I will review the impact it had on the eLISA study, and present summary of the report by Gravitational Observatory Advisory Team.

Oltean

Alexandre Le Tiec — 2016-06-21T19:23:23Z

Speaker : M. Oltean

Title : Entropy in classical mechanics, general relativity, and the gravitational two-body problem

Abstract : In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics, there are a number of theorems which have been proposed for proving the non-existence of entropy in the latter sense. We explicate, clarify and extend the proofs of these theorems, and then we show why these proofs fail in general relativity ; due to properties of the gravitational Hamiltonian and phase space measures, the second law of thermodynamics holds. As a concrete application, we focus on the consequences of these results for the gravitational two-body problem, and in particular, we prove the non-compactness of the phase space of perturbed Schwarzschild-Droste spacetimes. We thus identify the lack of recurring orbits in phase space as a distinct sign of dissipation and thus entropy production.

Evans

Alexandre Le Tiec — 2016-06-21T19:22:44Z

Speaker : C. Evans

Title : Further high-precision comparisons between perturbation calculations and PN theory for eccentric inspirals

Abstract : The latest results will be presented on high-precision comparisons between self-force/black hole perturbation theory and post-Newtonian theory for eccentric binaries. In some cases new exact terms are found out to 7PN order. Recent results go beyond energy fluxes at infinity and now include angular momentum flux at infinity and both energy and angular momentum fluxes at the horizon of the primary. Some discussion of extending calculations to Kerr will be made.

Fujita

Alexandre Le Tiec — 2016-06-21T19:21:51Z

Speaker : R. Fujita

Title : Radiation reaction effect on orbital parameters of a spinning particle in Kerr spacetime

Abstract : We derive the gravitational energy flux from a spinning particle in a circular orbit around the equatorial plane of a Kerr black hole using the post-Newtonian approximation in the first-order black hole perturbation theory. The equation of the motion of the particle is solved to the first order of the particle's spin using pole-dipole approximation. We will estimate how new terms in the energy flux affect the orbital evolution of the particle.

Bini

Alexandre Le Tiec — 2016-06-21T19:20:50Z

Speaker : D. Bini

Title : High-order analytical self-force calculations

Abstract : I will review some recent results obtained in collaboration with Thibault Damour and Andrea Geralico on high-order analytical self-force calculations for equatorial eccentric orbits in Schwarzschild and Kerr spacetimes (including their transcription into the EOB formalism and the comparison with numerical relativity computations). I will also summarize the works done since the past three years and give an indication to some open problems and "works in progress."

Popov

Alexandre Le Tiec — 2016-06-21T18:59:34Z

Speaker : A. Popov

Title : Renormalization for the self-potential of a charge in static space-times

Abstract : The self-force is a force originating from the coupling between the charge of a particle and the field that this charge induces. The field induced by the point particle diverges at the particle's location, and therefore a regularization method is required to calculate the correct (and finite) self-force from this diverging field. For this problem, formal expressions for the self-force have been derived for various types of fields. Some of them are reviewed in [Hikida:2005, Barack:2009]. Note also the zeta function method [Lousto:2000] and the "massive field approach" for the calculation of the self-force [Rosenthal:2004]. In the ultrastatic space-times the renormalization of the field of static charge can be realized by the subtraction of the first terms from DeWitt-Schwinger asymptotic expansion of a three-dimensional Euclidean Green's function [Khus:2007, Krasnikov:2008, Bezerra:2009, Popov:2010]. In this work a similar approach expands to the case of static space-times. In the framework of the suggested procedure one subtracts some terms of expansion of the corresponding Green's function of a massive scalar field with arbitrary coupling to the scalar curvature from the divergent expression obtained. The quantities of terms to be subtracted are defined by a simple rule — they no longer vanish as the field's mass goes to infinity. Such an approach is similar to renormalization introduced in the context of the quantum field theory in curved space-time [DeWitt:1965, Christensen:1978]. The Bunch and Parker method [Bunch:1979] is used for expansion of the corresponding Green's function of a scalar field. We also implement this method to calculate analytically the scalar self-force on a particle, which is held static in the background of some wormhole spacetimes.

W. Hikida, H. Nakano and M. Sasaki, Class. Quant. Grav. 22 S753 (2005)
L. Barack, Class. Quantum Grav. 26 213001 (2009)
C. O. Lousto, Phys. Rev. Lett. 84 5251 (2000)
E. Rosenthal, Phys. Rev. D 69 064035 (2004)
N. R. Khusnutdinov and I. V. Bakhmatov Phys. Rev. D 76 124015 (2007)
S. Krasnikov, Class. Quant. Grav. 25 245018 (2008)
V. B. Bezerra and N. R. Khusnutdinov, Phys. Rev. D 79 064012 (2009)
A. A. Popov, Phys. Lett. B 693 180 (2010)
B. S. DeWitt, Dynamical Theory of Groups and Field (Gordon & Breach, 1965)
S. M. Christensen, Phys. Rev. D 17 946 (1978)
T. S. Bunch and L. Parker, Phys. Rev. D 20, 2499 (1979)

Thornburg

Alexandre Le Tiec — 2016-06-21T18:56:50Z

Speaker : J. Thornburg

Title : Scalar self-force for highly eccentric orbits in Kerr spacetime

Abstract : We consider the problem of computing the self-force for a scalar-field particle on a bound eccentric orbit (which need not be a geodesic) in Kerr spacetime. We use the Barack-Golbourn-Vega-Detweiler effective-source regularization followed by an ("-mode") Fourier decomposition and a separate time-domain numerical evolution in 2+1 dimensions for each . We introduce a finite worldtube which surrounds the particle worldline and define our evolution equations in a piecewise manner so that the effective source is only used within the worldtube. Viewed as a spatial region the worldtube moves to follow the particle's orbital motion. Our numerical evolution uses Berger-Oliger mesh refinement with 4th order finite differencing in space and time. We use slices of constant Boyer-Lindquist time near the black hole, deformed to be asymptotically hyperboloidal and compactified near the horizon and . Our computational scheme allows computation for highly eccentric orbits, and should be generalizable to orbital evolution in the future. Our present implementation is restricted to equatorial geodesic orbits, but this restriction is not fundamental. We present numerical results for a number of test cases with orbital eccentricities as high as 0.98. In some cases we find large oscillations ("wiggles") in the self-force on the outgoing leg of the orbit shortly after periastron passage ; these appear to be caused by the passage of the particle close to the background Kerr black hole.

Diener

Alexandre Le Tiec — 2016-06-21T18:49:20Z

Speaker : P. Diener

Title : Progress on the numerical calculation of the self-force in the time domain

Abstract : The effective source approach to the self-force problem has proven to be a valuable tool in numerical calculations of the self-force in the time domain. The first self-consistent evolutions of a scalar charge in orbit around a Schwarzschild black hole were performed a few years ago using a finite difference code on a full multi-patch 3D grid. The main limitation of those simulations was the limited accuracy caused by the non-smoothness of the effective source across the particle. In this talk I will present the ideas and main ingredients of a new code based on the Discontinuous Galerkin method that overcomes the accuracy issue and present some new results.

Hopper

Alexandre Le Tiec — 2016-06-21T18:36:32Z

Speaker : S. Hopper

Title : Frequency domain techniques to analyzing unbound motion on Schwarzschild spacetime

Abstract : Numerically solving for the field sourced by unbound motion on a black hole background presents challenges distinct from those of bound motion. While time domain codes are largely "source agnostic" and adapt quite naturally to unbound motion, frequency domain techniques must be adjusted significantly. In particular, while the source and field are both decomposed as Fourier series when considering bound geodesic motion, unbound motion requires a Fourier transform, with a dense spectrum. More significantly, the frequency domain source terms are not confined to a finite range, which can lead to substantial technical challenges. I will present new methods to overcome these difficulties and consider the benefits (and drawbacks) of using frequency domain techniques to compute the self force for unbound sources.

Colleoni

Alexandre Le Tiec — 2016-06-21T18:35:46Z

Speaker : M. Colleoni

Title : Gravitational self-force along marginally bound orbits in Schwarzschild spacetime

Abstract : We present a first computation of the gravitational self-force along marginally bound orbits in Schwarzschild spacetime. We computed the conservative self-force correction to the azimuthal frequency of the innermost bound circular orbit (IBCO). The calculation required an integration of the self-force along a marginally bound (zero-binding-energy) orbit starting from infinity. Our result is consistent with the one that would follow by applying the so-called "first law of binary black hole mechanics" to the IBCO. We also describe how our numerical framework might be used to inform the conservative sector of the EOB model.