Ninth Capra Meeting on Radiation Reaction

Lior Burko, University of Alabama in Huntsville burko-at-uah.edu

The Capra series of meetings (named after the ranch in Southern California--that Caltech alumnus director Frank Capra bequeathed to his alma mater--the venue of the first meeting in 1998) are annual meetings on radiation reaction, that focus on the finite-mass corrections to the motion of a small mass in the gravitational field of a much larger mass, and on the emitted gravitational waves. In addition to being an interesting fundamental problem in general relativity, it is also a timely one, as some of the most promising sources for low frequency gravitational waves, that can be observed by space borne detectors such as LISA, are the waves emitted when a stellar mass compact object inspirals into a supermassive black hole at a galaxy's center. With a typical mass ratio of $10^{-6}$-$10^{-5}$, the description of these sources and their waveforms are the main motivation for the Capra meetings. The Ninth Annual Capra Meeting was hosted by the Center for Gravitation and Cosmology of the University of Wisconsin-Milawaukee from June 9 to 11, 2006 (and followed by the now traditional ``post Capra Workshop" June 12 to 14), and organized by Warren Anderson, John Friedman, Eirini Messaritaki, and Alan Wiseman. Administrative support was provided by Steve Nelson. In addition to the host Center, the meeting was supported financially by the Graduate School at UWM and by the Center for Gravitational Wave Astronomy at the University of Texas at Brownsville. The slides presented at the meeting are available online at the meeting's website, http://www.lsc-group.phys.uwm.edu/capra9/). The author of this Summary, and surely all the participants of this highly successful meeting, would like to thank the organizers, and especially Eirini Messaritaki, for all the hard work they have put in it.

Seventeen talks were presented. A number of talks were about various aspects of radiation reaction for particle motion in the spacetime of a Kerr black hole: Carlos Sopuerta (work with Pablo Laguna at Penn State) discussed advances in numerical simulations of extreme mass ratio inspirals, using finite element methods to handle spatial derivatives, and finite differences for the temporal derivatives. While in Schwarzschild very good agreement (to $0.05 \%$) with finite difference methods is found [1], in Kerr grid density adaptability is still a problem, that leads to accuracy problems.

One of the problems related to the so-called ``gauge problem" is that the full and singular parts of the gravitational field of a particle are often written in different gauges. One way to attack this problem is to find instead the Weyl scalars, which are gauge independent. Notably, the reconstruction of the metric perturbations from the Weyl scalars is problematic when a source particle is present, because there are more gauge conditions to satisfy than gauge degrees of freedom. However, if one obtains the regularized Weyl scalars, then one has a solution of the homogeneous Einstein equation, and therefore one doesn't have the above problem in reconstructing the metric perturbations. Then, the metric perturbations can be found in any gauge, because the Weyl scalars are gauge independent. Bernard Whiting (work with Larry Price at the University of Florida) reported on work in progress related to the finding of the metric perturbations in Kerr by first regularizing the Weyl scalars, specifically the jump conditions on the radiative modes of the Weyl scalars. Whiting focused on circular but non-equatorial orbits in Kerr. Using this method Whiting found the leading regularization parameter ``$A$", and work is in progress on finding the other parameters. John Friedman (work with Tobias Keidl and Alan Wiseman at UWM) addressed a closely related question, of how to find the regularized Weyl scalars using a special gauge that is exploiting the separability of the Teukolsky equation. Keidl (work with Friedman, Swapnil Tripathi, and Wiseman at UWM) then applied this approach to a simple case of a static mass point in the Schwarzschild spacetime, and showed how to solve the Bardeen-Press equation for $\Psi_4$. For the case of a static electric charge in Schwarzschild, this method successfully reproduces the result of Smith and Will [2].

Dong-Hoon Kim (AEI) discussed work in progress on a mode sum calculation of regularization parameters in Kerr, specifically for scalar field self force for generic orbits in Kerr. Kim describes the singular field in THZ normal coordinates [3], and finds the regularization parameters ``$A$", ``$B$", and ``$C$". Katsuhiko Ganz (Kyoto University, work with Wataru Hikida, Hiroyuki Nakano, and Takahiro Tanaka) addressed the adiabatic evolution of orbits in Kerr with large inclination angles, extending previous work in [4]. Ryuichi Fujita (work with Hideyuki Tagoshi at Osaka University) discussed a new method to integrate the Teukolsky equation in the frequency domain, that is based on the MST formalism [5], in which one expands the homogeneous solutions in hypergeometric functions near the horizon and in Coulomb wave functions near spatial infinity, and matches the solutions across an overlap region. Fujita applied the method to inclined orbits in Kerr with small eccentricity. For cases where fluxes are available from other methods, agreement to at least 6 significant figures is found. In Schwarzschild, agreement to 15 significant figures was reported [6].

Other talks discussed issues related to a Schwarzschild black hole: Lior Burko (UAH) discussed the evolution of quasi-circular orbits under a local self force, including conservative effects [7]. Nakano (Osaka University, work with Norichika Sago, Hikida, and Misao Sasaki) discussed the solution of the metric perturbations in the Regge-Wheeler gauge, including a change to the asymptotically-flat gauge for the non-radiative modes, and reported on a post Newtonian expansion for the radial component of the self force for a particle in circular orbit. Hikida (Kyoto University, work with Sanjay Jhingan, Nakano, Sago, Sasaki, and Tanaka) discussed the change in the orbital parameters of a scalar charge's motion under a self force, and obtained the latter in an expansion in the eccentricity. Hikida found that for small values of the eccentricity, the conservative effects on the phases are small, and are not likely to accumulate to $\pi$. However, gravitational conservative self force effects are expected to be larger than the scalar field counterpart. Steve Detweiler (work with Ian Vega at the University of Florida) discussed the gravitational self force effects on geodesics in Schwarzschild, extending previous work on the scalar field counterpart [8]. Vega (work with Detweiler) described work in progress on second-order gravitational perturbations due to a point particle, that is based on replacing the point particle with a small black hole at the world line.

Abraham Harte (Penn State) reported on work based on Dixon's formalism to evaluate self forces on extended bodies, which was applied to electromagnetism in flat spacetime [9]. Eric Poisson (work with Roland Haas at the University of Guelph) described a method for calculation of regularized self forces based on a tetrad decomposition of the singular field [10]. Instead of expanding a vector in vector harmonics, Poisson described its projection on an orthonormal tetrad, followed by an expansion in scalar harmonics. In a carefully chosen ``Cartesian" tetrad, only a finite number of coefficients are non-zero, which makes this formalism attractive. Haas described work in progress on the scalar self force for eccentric orbits in Schwarzschild based on a time domain calculation. Wiseman (work with Friedman, Keidl, and Tripathi at UWM and Samuel Gralla at Yale University and the University of Chicago) discussed the computation of the self force using a modification of the Quinn-Wald axioms, using a method based on finding an exact mode sum that represents the entire singular field. Carlos Lousto (UTB) reviewed the recent exciting advances in numerical relativity [11].