| Abstracts |
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| Mino: For LISA project, a theoretical prediction of the orbital evolution around a supermassive blackhole is necessary. For this calculation, one of promising approaches is to calculate the self-force acting on the particle. By extending the Regge-Wheeler formulation of the metric perturbation, we present a simple and practical calculation method. |
| Barack: I will survey the current status of the "mode-sum approach" for calculating the gravitational self-force. In particular, I will report on (1) the derivation of all "regularization parameters" for a generic orbit in Schwarzschild; (2) the full implementation of the mode-sum scheme in the test-case of radial trajectories, and in the case of circular orbits (the latter still in progress); (3) the use of a large-l analytic approximation for improving the convergence rate of the mode-sum series; and (4) the "gauge problem" and our way of handling it in Schwarzschild spacetime. |
| Burko: I will compare the orbital evolution of a point particle in quasi-circular equatorial orbit around a Schwarzschild black hole using two approaches for a radiation-damped orbit: i) making use of just the dissipative piece of the self-force, which is equivalent to methods based on balancing quantities which are otherwise constants of motion, and ii) making use of the full self-force, including both dissipative and conservative effects. This comparison is applicable for point particles carrying charge of any spin. I will show how relevant observational quantities are different, and present the resulting waveforms. I will also discuss the relevance for LISA. |
| Lousto: We compute the gravitational self-force (or ``radiation reaction'' force) acting on a particle falling radially into a Schwarzschild black hole. Our calculation is based on the ``mode-sum'' method, in which one first calculates the individual l-multipole contributions to the self-force (by numerically integrating the decoupled perturbation equations) and then regularizes the sum over modes by applying a certain analytic procedure. We demonstrate the equivalence of this method with the $\zeta-$function scheme. The convergence rate of the mode-sum series is considerably improved here (thus notably reducing computational requirements) by employing an analytic approximation at large l. (with Leor Barack) |
| Detweiler: The self force contributes to the orbital frequency, energy and angular momentum at O(mu/M). In the context of a circular orbit about a non-rotating black hole, these effects are "relatively easy" to calculate to high precision using the Regge-Wheeler perturbation formalism. The computational effort is greatly reduced by using an extension of the Barack-Ori regularization procedure which results in rapid convergence of the sum over l-modes. |
| Poisson: Fermi normal coordinates are constructed in a neighborhood of a reference world line by considering spacelike geodesics that intersect the world line orthogonally. Here we consider an alternative construction that involves null geodesics instead. As I shall describe in this talk, this coordinate system is especially well suited to self-force calculations. |
| Campanelli: We investigate higher than the first order gravitational perturbations in the Newman-Penrose formalism. Equations for the Weyl scalar $\psi_4,$ representing outgoing gravitational radiation, can be uncoupled into a single wave equation to any perturbative order. For second order perturbations about a Kerr black hole, we prove the existence of a first and second order gauge (coordinates) and tetrad invariant waveform, $\psi_I$, by explicit construction. This waveform is formed by the second order piece of $\psi_4$ plus a term, quadratic in first order perturbations, chosen to make $\psi_I$ totally invariant and to have the appropriate behavior in an asymptotically flat gauge. $\psi_I$ fulfills a single wave equation of the form ${\cal T}\psi_I=S,$ where ${\cal T}$ is the same wave operator as for first order perturbations and $S$ is a source term build up out of (known to this level) first order perturbations. We discuss the issues of imposition of initial data to this equation, computation of the energy and momentum radiated and wave extraction for direct comparison with full numerical approaches to solve Einstein equations. (with Carlos Lousto) |
| Whiting: Traditional calculations of radiation reaction involve the calculation of a regularized field which is C^0. At the location of a compact source,derivatives of this are not well defined, and averaging is usually involked in the calculation of a self force. While averaging provides a pragmatic resolution of the underlying difficulty, it does not naturally lead to the definition of a smooth geometry in which radiation reaction effects direct the compact object on an adjusted geodesic (or Lorentz force path in the case of a charged particle). Recently it has become possible to rectify this situation in a highly significant way. The singular part of the retarded Green's function can be determined locally, and can now be subtracted off in such a way that what remains behind is smooth and differentiable. In principle, it is a solution of the homogeneous equation. This means that the perturbed field, near the compact object, is also a homogeneous gravitational perturbation, which is likewise smooth and differentiable. In the associated, perturbed spacetime, the compact object follows a geodesic. In practice, finite approximations in the subtraction lead to a result with less than the requisite amount of smoothness. Direct knowledge of how a better approximation can improve the resulting smoothness also leads to greatly increased numerical convergence for the regularized remainder, following the subtraction of the singular part. Proposed application of this result to the Kerr spacetime (with Steve Detweiler) will be discussed. |
| Jones: In this talk I will present the results of a linear Newtonian hydrodynamics code in which the dissipative effect of gravitational wave emission is modelled using a local force. The force itself is that derived via post-Newtonian methods by Blanchet, Damour and Schafer, who eliminated the high time derivatives found in other formulations by introducing a number of Poisson-like equations. It is hoped that by testing this method in the linear regime it can then be easily extended and used with confidence is the non-linear one. |
| Miller: The field of numerical relativity has advanced to the point where we can now numerically evolve binary neutron star configurations for over 10 orbital periods. Here, we compare the orbital decay rate of fully general relativistic neutron star binaries with the decay rates predicted by Post-Newtonian approximations and the so-called ``conformally flat quasi-equilibrium'' approximations. |
| Martel: Solar-mass black-holes and/or neutron stars are among the strongest candidates for successful detection by LISA. This type of event is well described in the framework of perturbation theory. In this framework, one considers the solar-mass black hole and/or the neutron star a source for the perturbations which evolve in a Kerr background. This leads to the well known Teukolsky equation, with a source term constructed from the four-velocity of the perturbing object. The source term is therefore a distribution which can lead to potential problems when numerically-solving the Teukolsky equation. These can be avoided by replacing the Dirac delta-functions by Gaussian pulses. The question is then to determine under which conditions this simplification is justified and results in accurate waveforms. This can be addressed by evolving the perturbations due to a scalar charge in a Schwarzschild background. This is convenient because spherical symmetry reduces the inhomogeneous scalar wave equation to 1+1 wave equation which can be numerically integrated either with a singular source term or with a Gaussian pulse approximating the Dirac delta-function in the source term. I will also discuss efforts made to integrate the inhomogeneous Teukolsky equation in the Kerr background. |