Bulletin of the American Physical Society
2008 APS April Meeting and HEDP/HEDLA Meeting
Volume 53, Number 5
Friday–Tuesday, April 11–15, 2008; St. Louis, Missouri
Session E10: Self Force and Gravitational Wave Tails |
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Sponsoring Units: GGR Chair: Eric Poisson, University of Guelph Room: Hyatt Regency St. Louis Riverfront (formerly Adam's Mark Hotel), St. Louis A |
Saturday, April 12, 2008 3:30PM - 3:42PM |
E10.00001: Gravitational self-force calculations in the time domain in 2+1D: progress report Leor Barack, Lior M. Burko The goal of this work is to calculate the gravitational self force acting on a point mass in motion in the spacetime of a Kerr black hole in the Lorenz gauge. We decompose the field into azimuthal $m$-modes, which leads to separable wave equations in Kerr. Individual $m$-modes of the metric perturbations diverge logarithmically (in the proper distance from the point particle), and practical regularization of the individual m-modes may be done using a ``puncture function," a method that has been found to be efficient in the context of the toy model of scalar-field self forces for circular orbits in Schwarzschild. The $m$-mode approach has several advantages, most notably the amenability to numerical solutions in the time domain, thus benefiting from experience gained by several groups in the numerical solution of linearized wave equations on a Kerr background in the time domain in 2+1D, and the adaptability to more complex orbits, including generic ones. As a first step we implement this program for the simpler context of circular orbits in Schwarzschild. Notably, we do not exploit the spherical symmetry of the Schwarzschild backgound or the symmetry of the orbit. Instead, we construct the scheme so that generalizations to either more complex orbits or to Kerr spacetime are susceptible of implementation at later stages, and work in 2+1D. This talk is a progress report on work still ongoing. [Preview Abstract] |
Saturday, April 12, 2008 3:42PM - 3:54PM |
E10.00002: Power-law tails in the Kerr spacetime Richard Price, Reinaldo Gleiser, Jorge Pullin In the Schwarzchild spacetime, compact initial perturbations evolve to ``tails'' that decay as $t^{-n}$. We present new numerical and analytic results that clarify the value of $n$, and the features of the spacetime on which $n$ depends. [Preview Abstract] |
Saturday, April 12, 2008 3:54PM - 4:06PM |
E10.00003: Late--time Kerr tails revisited Lior M. Burko, Gaurav Khanna Numerous conflicting results ---both analytical and numerical--- have been reported on the decay rate of late time tails in the Kerr spacetime. In particular, there has been much disagreement on whether the decay rate of an initially pure multipole moment ${\ell}$ is according to $t^{-(2{\tilde\ell}+3)}$, where ${\tilde\ell}$ is the least multipole moment whose excitation is not disallowed, or whether the decay rate is according to $t^{-n}$, where $n=2\ell +3$ if $\ell -m < 2$, $n=\ell +m+1$ if $\ell -m\ge 2$ is even, and $n=\ell +m+2$ if $\ell -m\ge 2$ is odd. The answer to this question is very sensitive to the details. In particular, it is very important whether one specifies the velocity or the momentum of the field as part of the initial--data set. We do careful 2+1D numerical simulations, and find the tails decay--rate for the case that has become the testbed of such studies, specifically an initially pure $\ell=4$, $m=0$ multipole on a Boyer--Lindquist or ingoing Kerr time slices. We also consider other cases, including non--azimuthal ones, such as an initial $\ell=6$, $m=2$ multipole. We emphasize some of the causes for potential errors in 2+1D simulations and argue that conflicting past results may be attributed to them. Specifically, we discuss the misidentification of an intermediate tail as an asymptotic one and the misidentification of noise evolution as that of a signal. We then show that our simulations are free of such errors. [Preview Abstract] |
Saturday, April 12, 2008 4:06PM - 4:18PM |
E10.00004: Regularization of fields for self-force problems in curved spacetime: foundations and a time-domain application Ian Vega, Steven Detweiler We report on recent tests of a new approach towards the calculation of self-forces and waveforms arising from moving point charges in curved spacetimes. As opposed to mode-sum schemes that regularize the self-force derived from the singular retarded field, this approach regularizes the retarded field itself. The singular part of the retarded field is first analytically identified and removed, yielding a finite, differentiable remainder from which the self-force is easily calculated. This regular remainder satisfies an effective wave equation which enjoys the benefit of having a non-singular source. Our method of field regularization then involves directly solving this effective wave equation for the remainder, which avoids the difficulties associated with numerical models for singular sources, while providing easy access to the self-force on the charge without the need for further regularization or slowly-convergent mode sums. In this talk, we shall discuss our preliminary implementation of this method using a 4th-order (1+1) code applied to the simple case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. Comparisons with highly-accurate, frequency-domain results indicate agreement to $\sim 0.1\%$. [Preview Abstract] |
Saturday, April 12, 2008 4:18PM - 4:30PM |
E10.00005: Finding Fields and Self-Force in a Gauge Appropriate to Separable Wave Equations I Larry Price, Tobias Keidl, Dong Hoon Kim, John Friedman, Eirini Messaritaki, Alan Wiseman Gravitational radiation from the inspiral of a stellar mass sized black hole into a supermassive rotating black hole is an important candidate for detection with the proposed Laser Interferometer Space Antenna. A complete and self-consistent description of the motion of the particle requires knowledge of the gravitational self-force. We report progress on computing the self-force from a method based on regularizing solutions to the Teukolsky equation. In this talk, we focus on describing the general procedure for computing the self-force in the Kerr spacetime. [Preview Abstract] |
Saturday, April 12, 2008 4:30PM - 4:42PM |
E10.00006: Finding Fields and Self-Force in a Gauge Appropriate to Separable Wave Equations II Tobias Keidl, John Friedman, Dong-Hoon Kim, Eirini Messaritaki, Larry Price, Alan Wiseman Gravitational waves from the inspiral of a stellar-sized black hole in to a supermassive black hole are an important source for the Laser Interferometer Space Antenna. A method for computing self force has been proposed that uses regularizes solutions of the Teukolsky equation [1]. The prescription is outlined in the previous talk. In this talk, I focus on computational details for a particle in circular orbit in a Schwarzschild spacetime. \newline [1] T.\ S.\ Keidl, J.\ L.Friedman, and A.\ G.\ Wiseman, Phys. Rev. D. {\bf 75}, 124009 (2007); gr-qc/0611072. [Preview Abstract] |
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