1 / 9

2006 Midwest Relativity Meeting Tobias Keidl University of Wisconsin--Milwaukee

On finding fields and self force in a gauge appropriate to separable wave equations (gr-qc/0611072). 2006 Midwest Relativity Meeting Tobias Keidl University of Wisconsin--Milwaukee In collaboration with: John Friedman, Eirini Messaritaki , Alan Wiseman. Motivation.

mare
Télécharger la présentation

2006 Midwest Relativity Meeting Tobias Keidl University of Wisconsin--Milwaukee

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. On finding fields and self force in a gauge appropriate to separable wave equations(gr-qc/0611072) 2006 Midwest Relativity Meeting Tobias Keidl University of Wisconsin--Milwaukee In collaboration with: John Friedman, Eirini Messaritaki,Alan Wiseman

  2. Motivation Laser Interferometer Space Antenna (LISA) • Dedicated space-based gravitational wave observatory • Launch date ~2014-2020 • 5 year expected lifetime

  3. Motivation • Look for Extreme MassRatio Inspirals • Estimate LISA will see ~10-1000 events per year (J.R. Gair et al 2004) • Develop waveforms templates suitable for LISA to detect gravitational waves • Inspiral can be modeled within perturbation theory • Can treat captured object as a small point perturbation on the background spacetime Graphic stolen from www.srl.caltech.edu

  4. Point Particle Regularization • Regularized gravitational self-force MiSaTaQuWa Mino，Sasaki and Tanaka (‘97) Quinn and Wald (‘97) • Detweiler and Whiting (‘03) particle follows geodesic of hrenormalized Known only for Harmonic gauge Gauge dependent Need to solve 10 coupled PDEs

  5. Teukolsky Formalism • For a background Kerr black hole, there are two complex projections of the perturbed Weyl tensor are gauge independent: 0,4 • Solvable by a use of the Teukolsky equation (written below for 4 in Schwarzschild) • Related to the metric by a 2nd order differential operator

  6. Point Particle Regularization Gauge Independent Solve Teukolsky equation numerically Calculate from Harmonic gauge or directly

  7. But… • This method gives us 0 or 4, not the metric • In vacuum, there is a prescription for reconstructing the metric from 0 or 4 • 0 or 4 do not determine the s=0,1 piece • Use jump condition across particle across spin 0 and 1 projections of the Einstein equations to fix remaining metric pieces (Price, Shankar and Whiting)

  8. Radiation Gauge Metric • Work by Chrzanowski, Kegeles & Cohen, Wald, Lousto & Whiting, Ori • Can use a formalism by Kegeles and Cohen to construct a scalar potential from 0 or 4 • “Ingoing Radiation Gauge” metric

  9. Outline of Calculation • Compute 4ret from Teukolsky Equation • Use hsingular in harmonic gauge to compute 4sing • 4ren = 4ret - 4sing is a sourcefree solution to the Teukolsky equation • Calculate renormalized metric from 4ren • Use jump condition on the Einstein equations to find s=0,1 piece of metric • Calculate self force from perturbed geodesic equation

More Related