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 Mass Ratio 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 h renormalized Gauge dependent Known only for Harmonic gauge 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 IndependentCalculate from Harmonic gauge or directly Solve Teukolsky equation numerically

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. 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 Radiation Gauge Metric

9. Outline of Calculation 1.Compute  4 ret from Teukolsky Equation 2.Use h singular in harmonic gauge to compute  4 sing 3.  4 ren =  4 ret -  4 sing is a sourcefree solution to the Teukolsky equation 4.Calculate renormalized metric from  4 ren 5.Use jump condition on the Einstein equations to find s=0,1 piece of metric 6.Calculate self force from perturbed geodesic equation