Fourth Capra Meeting on Radiation Reaction

Lior Burko, California Institute of Technology
burko@tapir.caltech.edu

The Capra meetings on radiation reaction are annual gatherings, the fourth of which was hosted by Carlos Lousto at the Albert-Einstein-Institut in Golm, Germany, May 28-31, 2001. The first meeting in this series was held in 1998 at a ranch in northeastern San Diego county in California. This ranch was once owned by Frank Capra, the 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. In the tradition of the ``Texas'' meetings, each meeting in this series is called a ``Capra'' meeting, even if the venue is rather removed from Capra's ranch. Summaries of previous Capra meetings appeared in Matters of Gravity, No. 14 (Fall 1999) (Capra2 by P. Brady and A. Wiseman) and No. 16 (Fall 2000) (Capra3 by E. Poisson).

The Capra meetings focus on radiation reaction and self interaction in general relativity. The motivation for this topic is twofold. First, the two-body problem in general relativity is as yet an unresolved problem. Even the restricted two-body problem, where the mass ratio of the two bodies is extreme, lacks in understanding. It is this restricted problem which the Capra meetings focus on. In the limit of infinite mass ratio, a test mass moves along a geodesic of the spacetime created by the massive body. When the mass ratio is finite, the energy-momentum of the small mass acts as an additional source for spacetime curvature, which affects the motion of the small mass itself. Specifically, the small mass now moves along a geodesic of a perturbed spacetime. An alternative viewpoint is to construe the motion of the small mass as an accelerated, non-geodesic motion in the unperturbed spacetime of the big mass. This acceleration is then caused by the self force of the small mass. Although for many interesting cases it is sufficient to restrict the discussion to linearized perturbations (thanks to the high mass ratio), there still remains an inherent difficulty: the metric perturbations typically diverge at the coincidence limit of the field's evaluation point and the source of the perturbations. It is the removal of this divergence, or the regularization problem of the self force, which constitutes the greatest hurdle in the solution of the restricted two-body problem.

The second motivation stems from the prospects of detecting low-frequency gravitational waves with the Laser Interferometer Space Antenna (LISA), which is currently scheduled to fly as early as 2010. One of the most interesting potential sources for LISA is the gravitational radiation emitted by a compact object spiraling into a super-massive black hole, like those in galaxy centers. The typical mass ratio is then , which makes the restricted two-body problem relevant. During the last year of inspiral (the LISA integration time) the system can undergo orbits. In order to generate accurate templates which track the system over so many orbits, it is required to compute the orbital evolution (due to both dissipative and conservative effects) to high accuracy, which requires the inclusion of self interaction.

Twenty talks, covering many aspects and approaches to the problem, were given at the fourth Capra meeting. The following short description is greatly biased by my own understanding and taste. A full list of the talks, including the online proceedings of the meeting (namely, links to the slides used by the speakers), appears at the meetings web page: http://www.aei-potsdam.mpg.de/~lousto/CAPRA/Capra4.html

A number of different approaches for the calculation of the self force have been suggested. These are approaches for the computation of the ``tail'' part of the self force [1,2]. M. Sasaki, Y. Mino, and H. Nakano presented progress obtained in Power-Expansion Regularization. M. Sasaki described, in addition to Power-Expansion Regularization also an alternative approach of Mode-by-Mode Regularization, and also discussed the problems of extending the work to Kerr background, and the difficult gauge problem. Y. Mino described in great detail the mathematical techniques which are needed for Power-Expansion Regularization. H. Nakano showed how to apply this approach for the computation of the self force acting on a scalar charge in circular orbit around a Schwarzschild black hole [3]. L. Barack described his work with A. Ori on the extension of Mode-Sum Regularization to the gravitational case [4], and L. Burko discussed work with Y.-T. Liu on how Mode-Sum Regularization can be applied for the case of a static scalar charge in the spacetime of a Kerr black hole, even without knowledge of the Mode-Sum regularization function [5]. W. Anderson presented progress obtained with É. Flanagan and A. Ottewill in the approach of normal neighborhood expansion. A. Ori presented work with E. Rosenthal on extended-body models, and showed how to re-derive the Abraham-Lorentz-Dirac equation (in flat spacetime) using such models, based on momentum considerations. This approach appears to be very promising also in curved spacetime. C. Lousto discussed -function regularization [6]. In all these different approaches to the self force there was significant progress since the previous Capra meeting, although clearly much more work is still needed.

A second, exciting direction which was emphasized for the first time in the fourth Capra meeting, is the need for demonstrating the connection between the different methods. This is important not just in order to demonstrate the consistency and viability of the different approaches, but also in order to compare their computational effectivenesses, and perhaps even allow for a synergy of two or more approaches. S. Detweiler proposed a (short) list of benchmark problems, which he encouraged all the people who are working in this field to consider, in order to confront and compare the different approaches. Specifically, this list includes the problem of a scalar charge in circular orbit around a Schwarzschild black hole, and the calculation of gauge invariant quantities in the gravitational analogue. It is hoped that much insight can be gained by such comparisons. For the former benchmark problem one can already compare the work by Nakano, Mino, and Sasaki [3] with earlier work by Burko [7], and hopefully other researchers will consider this problem too. A different way of comparing different approaches is to compare the infinities which are removed. Specifically, in the approach of Power-Expansion regularization one computes the direct part of the self force. In Mode-Sum Regularization one typically computes the so-called regularization function using local integrations of the Green's function. As the two should agree, work is now in progress to show just that.

Other interesting talks were given by A. Wiseman, who showed that the self force on a static scalar charge in Schwarzschild spacetime is exactly zero also when the scalar field is not minimally coupled (despite earlier results by Zel'nikov and Frolov [8], and by B. Whiting, who discussed how to extend the Chrzanowski method to the time domain, and perhaps also include sources. G. Schaefer described work with Damour and Jaranowski on a post-Newtonian approach to radiation reaction, J. Levin discussed the fate of chaotic binaries, C. Glampedakis described work with D. Kennefick on a `circularity theorem' for spinning particles in Kerr spacetime, J. Pullin described a code in the time domain to obtain radiation reaction waveforms, N. Andersson described r-modes as a source of gravitational radiation, and C. Cutler described gravitational wave damping of neutron star precession. S. Detweiler talked about gravitational self-force on a particle in Schwarzschild spacetime, E. Poisson described work with M. Pfenning on the self force in the weak-field limit [9] , and B. Sathyaprakash discussed resummation techniques for the binary black hole problem.

** References:**

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

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

[3] H. Nakano, Y. Mino and M. Sasaki, gr-qc/0104012

[4] L. Barack, gr-qc/0105040

[5] L. M. Burko and Y. T. Liu, Phys. Rev. D ** 64**, 024006
(2001)

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

[7] L. M. Burko, Phys. Rev. Lett. ** 84**, 4529 (2000)

[8] A. I. Zel'nikov and V. P. Frolov,
Sov. Phys. JETP ** 55**, 191 (1982)

[9] M. J. Pfenning and E. Poisson,
gr-qc/0012057