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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.

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

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  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

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