# 3rd Capra Meeting

# Tapir, Caltech

# 5-9 of June of 2000

The reconstruction of this webpage was only possible due to the efforts led by Scott Hughes and contributions from Patrick Brady, Eanna Flanagan, Eric Poisson and Bernard Whiting.

## Announcement

The 3rd Capra Ranch Meeting on Radiation Reaction will be held at the California Institute of Technology, from June 5th to June 9th, 2000. It will immediately follow the KipFest, the symposium being held at Caltech from June 1st to June 3rd in honor of Kip Thorne's 60th birthday [KipFest Link]. We hope that people attending the KipFest will decide to stay a few extra days and attend Capra 3 as well.

As in previous years, the primary focus of the meeting will be on radiation reaction in general relativity. However, we encourage talks that are tangential to this primary focus. We will also follow the very successful, highly informal format used in previous meetings: equal time will be allotted to talks and discussion. We expect and hope that the distinction between "talk" and "discussion" will be an artificial one - as at the past meetings, we encourage discussion during talks, blending together into a highly interactive session.

In order to facilitate discussion, the number of talks will be limited to no more than four per day. We therefore must limit the number of speakers to 16. We encourage people who will not be giving a talk to attend and participate in the discussions. There will be no formal proceedings; a web archive of talks will be placed online, as has been done for the 2nd Capra Meeting (http://www.lsc-group.phys.uwm.edu/~patrick/ireland99/index.html ).

There will be no registration fee, and the organizers cannot provide financial support for any participants. Refreshments will be provided at coffee breaks, but meals will be the responsibility of individual participants.

## Historical Note

The first meeting in this series was held in August 1998 at a ranch in northeastern San Diego county. This ranch was once owned by Frank Capra, the American director of such movies as ``Mr. Smith Goes to Washington'' and ``It's a Wonderful Life''. Capra was a Caltech alumnus, and donated the ranch to Caltech. The second meeting was held in August 1999 at University College Dublin, Ireland. In the tradition of the ``Texas'' meetings, we call each meeting in this series a ``Capra'' meeting, even if the venue is rather removed from Capra's ranch.

## Participants

Adrian Ottewill

Alan G. Wiseman

Alessandra Buonanno

Alessandro Spallicci

Amos Ori

Amos Harpaz

Ben Owen

Bernard F. Schutz

Brien Nolan

B S Sathyaprakash

Carlos Lousto

Dan Kennefick

Eanna E. Flanagan

Eric Poisson

Hiroyuki Nakano

Jolien Creighton

Kip Thorne

Kostas Glempedakis

Leonid Grishchuk

Leor Barack

Lior Burko

Manuela Campanelli

Neil Cornish

Nils Andersson

Patrick Brady

Richard Price

Scott Hughes

Steve Detweiler

Thomas Hertog

Warren Anderson

Yasushi Mino

## Talks

Patrick R. Brady - Point-splitting regularization of the radiation reaction - with Warren Anderson and Alan Wiseman

## Organisers

Scott Hughes

Lior Burko

## Post Conference Summary

# Third Capra Meeting on Radiation Reaction

Eric Poisson, University of Guelph

The Capra series of meetings on radiation reaction in curved spacetime were initiated in 1998 by Patrick Brady. The first meeting was held at Frank Capra's ranch in southern California, and the name stayed, even though the location of the meeting has changed. (Frank Capra is the famous movie director who made such films as ``It's a wonderful life'' and ``Mr. Deeds goes to town''. Capra had studied at Caltech before going to Hollywood; he bequeathed his ranch to his alma mater, which passed to Caltech upon his death.) The second meeting was held in Dublin, Ireland, and was organized by Adrian Ottewill. This latest installment was held at Caltech June 5-9, 2000, and was organized by Lior Burko and Scott Hughes. Here I will present a rather broad overview of the main issues discussed during the meeting, and highlight just a few of the contributions. The complete proceedings -- a copy of the slides presented by all the speakers -- can be found at the meetings's web site: http://www.tapir.caltech.edu/~capra3/. This series of meetings is concerned with the motion of a small mass in a strong gravitational field. It is known that in the limit of vanishing mass, the particle moves on a geodesic of the background spacetime. Away from this limit, however, the motion in the background is no longer geodesic, and can be described in terms of a self-force. (In some sense, the motion is geodesic in the perturbed spacetime, which consists of the background plus the perturbation created by the particle. For a point particle, however, the perturbation is singular at the particle's location, and careful thought must be given to the removal of the singular part of the field, which does not affect the motion. In flat spacetime, this subtraction gives rise to the well-known half-retarded minus half-advanced potential.) The main focus of the meeting was the practical computation of this force. While this problem raises many interesting issues of principle (such as the removal of the singular part of the metric perturbation created by a point particle), there is also a practical necessity. The detailed modeling of gravitational waves produced by a solar-mass compact object orbiting a massive black hole requires an accurate representation of the orbital motion, which evolves as a result of radiation loss. In the generic case involving a rapidly rotating black hole, this evolution must be calculated on the basis of a radiation-reaction force. Such sources of gravitational waves will be relevant for the Laser Interferometer Space Antenna (LISA), a space-borne detector designed to measure low-frequency waves (it has a peak sensitivity at around 1 mHz). The electromagnetic analogue to this problem was solved in 1960 by DeWitt and Brehme [1], who derived a curved-spacetime expression for the self-force acting on a point electric charge. The gravitational self-force was obtained much more recently, first by Mino, Tanaka, and Sasaki [2], and then by Quinn and Wald [3]. There is also a similar force in the case of scalar radiation, which was calculated by Quinn [4]. In all three cases the self-force is expressed as an integral over the past world-line of the particle, and the integral involves the nonsingular part of the retarded Green's function, which has support inside the past light cone of the particle's current position. The explicit evaluation of only this part of the Green's function is challenging, however, and a good portion of the meeting was devoted to this issue. A plausible method for calculating the Green's function involves a separation-of-variable approach made possible by the symmetries of the black-hole spacetime. (Thus far, all calculations have been restricted to the case of a Schwarzschild black hole). It is a simple matter to derive and solve the ordinary differential equation that governs each mode of the Green's function. The problem lies with the fact that the sum over all modes doesn't converge. (This is essentially because the individual modes do not distinguish between the singular and nonsingular parts of the Green's function.) Amos Ori, Leor Barack, and Lio Burko [5] have devised a way of regulating the mode sum, so as to extract something meaningful. Their results for simple situations involving scalar radiation were presented at the meeting, and are extremely promising. A similar regularization method was used by Carlos Lousto [6], who calculated the gravitational self-force acting on a radially infalling particle in Schwarzschild spacetime. Regularization was also exploited by Hiroyuki Nakano and Yasushi Mino to calculate the gravitational self-force in the weak-field limit. Insight into the self-force problem can be gained by adopting a more local point of view, and focusing on the immediate vicinity of the particle. Such an approach permits a clear identification of the singular part of the particle's field, which can then be decomposed into modes and subtracted from the full field. Such a strategy was adopted by Steve Detweiler (in the gravitational case) and by Patrick Brady (in the scalar case). A variation on this theme is to start with the Mino et al. expression for the gravitational self-force [2], and to evaluate the contribution to the world-line integral that comes from the particle's very recent past. Results along those lines were presented by Warren Anderson. The third Capra meeting has shown that the radiation-reaction problem is progressing very nicely. There are still many issues left to sort out, but it is nice to see that concrete results have now been obtained. I expect that progress will be swift in the coming year, and that the fourth (perhaps last?) meeting will be just as exciting as the preceding ones.

References:

[1] B.S. DeWitt and R.W. Brehme, Ann. Phys. (NY) 9, 220 (1960).

[2] Y. Mino, M. Sasaki, and T. Tanaka, Phys. Rev. D 55, 3457 (1997).

[3] T.C. Quinn and R.M. Wald, Phys. Rev. D 56, 3381 (1997).

[4] T.C. Quinn, gr-qc/0005030.

[5] See, for example, L.M. Burko, Phys. Rev. Lett. 84, 4529 (2000), and L. Barack, gr-qc/0005042.

[6] C.O. Lousto, Phys. Rev. Lett. 84, 5251 (2000).

Eric's conference report, along others from that time, can be found on the Matters of Gravity Newsletter of the Topical Group on Gravitation of the American Physical Society.

The reconstruction of this webpage was only possible due to the efforts led by Scott Hughes and contributions from Patrick Brady, Eanna Flanagan, Eric Poisson and Bernard Whitting.