The Capra meetings are devoted to the study of radiation reaction in General Relativity, a key problem in order to understand the general-relativistic dynamics of a two-body system. Probably, the main application of these studies is the description of the inspiral dynamics of stellar-mass compact objects into massive black holes in galactic centers, also known as extreme-mass-ratio inspirals (EMRIs), a primary scientific target for the future ESA/NASA Laser Interferometer Space Antenna (LISA) mission. Simulating EMRIs we can obtain gravitational waveform templates that will be crucial for the analysis of the LISA data. The scientific outcome of these observations ranges from tests of the no-hair theorem for black holes to the determination of stellar populations and the study of dynamics of galactic nuclei. In this sense, the Capra meetings and the community created around them has contributed much of the progress in the understanding of the radiation reaction problem and in the description of the dynamics and gravitational-wave emission of EMRIs.
The Capra series of meetings started in August 1998 at a ranch in northeastern San Diego county once owned by Frank Capra, the celebrated American film director, a Caltech alumnus who donated the ranch to Caltech, hence the name of the meeting. The series continued at the following venues: UCD, Dublin (1999); Caltech, Pasadena (2000); AEI, Potsdam (2001); Penn State, State College (2002); YITP, Kyoto (2003); CGWA, Brownsville (2004); RAL, Abingdon (2005); and UWM, Milwaukee (2006).
This year, the tenth edition of the Capra Meeting and Workshop took place at the University of Alabama in Huntsville, from June 24th to June 29th, 2007. It was organized by Lior Burko and was funded by the College of Science of the University of Alabama in Huntsville. Special thanks go to Jack Fix, and to Cindy Brasher and Dora Wynn for administrative support. The meeting was attended by 26 researchers from research/academic institutions in 7 countries.
Following the tradition of previous years, the meeting consisted of two parts: In the first one (June 25-27) the participants presented research talks, whereas the second one (June 27-29) was a workshop aimed at facilitating discussions, brainstorming, and collaboration. The program and an electronic version of all talks are available online at:
This year's meeting can be characterized by the amount of numerical work presented, especially in the time domain, which illustrates the progress in the field, in the sense that we are in a period in which a substantial part of the efforts are directed towards the numerical implementation of the analytical developments of past research by the Capra community. Another highlight of the conference was the celebration of the 60th birthday of Steve Detweiler, one of the main contributors to the Capra community and, after this year's edition, the person with most attendances at the meeting.
The meeting started with a summary by Leor Barack (Southampton) of the progress that the Relativity group at Southampton is making in the development of techniques and numerical algorithms, in the time domain, for the computation of the self-force. The talk served as an introduction to the presentations of the other Southampton group members present at the meeting. The first one was Norichika Sago, who presented work on the numerical calculations of the gravitational self-force, in the Lorenz gauge, for a particle orbiting a Schwarzschild black hole. The case of circular orbits has been completed  and the case of generic (eccentric) orbits is well underway. Darren Golbourn, also from Southampton, gave a talk on a new technique to regularize the self-force due to scalar-field perturbations from a particle orbiting a non-rotating black hole and its numerical implementation . This work is done using a 2+1 spacetime domain, which paves the way for a future extension to the case of a spinning Kerr black hole. The technique proposed consists of subtracting from each azimuthal mode of the retarded field a piece that describes the singular behavior of the scalar field near the particle. This is done through a careful analytical analysis of the scalar field near the particle, which is referred to by the authors as a puncture scheme, and indeed it resembles the puncture approach used in simulations in numerical relativity. After the break, Ian Vega (Gainesville) presented work along the same lines as the previous talk but using a different approach. In this talk the regularization procedure is based on the use of smeared-out sources in the scalar field equations, in the sense that the practical implementation consists of applying a window function to an analytical approximation to the singular part of the scalar field (the approximation is constructed using THZ coordinates). This also leads to an equation for the regular part involving an extended non-singular source. The numerical calculations are done using an evolution code in a 1+1 spacetime domain. Lior Burko (Hunstville) discussed progress in the time-domain extraction of extreme-mass-ratio binary waveforms by means of a Teukolsky numerical code in a 2+1 domain and two ways of regularizing the particle sources: (i) considering a smeared-out source based on the use of a Gaussian as an approximation to the Dirac delta distribution , and (ii) using a discretized version of the Dirac delta distribution that has a finite support in the computational domain . These calculations improve substantially the accuracy achieved with previous computational schemes.
The second day was opened by Paul Anderson (Wake Forest) with a talk on the calculation of the self-force using the Hadamard-WKB expansion. This is a completely analytic technique and the aim is to compute the non-local contribution to the self-force (tail term) by means of a quasi-local expansion. The case of a particle subject to a scalar field was shown as an illustration, and included a discussion of the range of validity of this type of expansion. Ted Newman (Pittsburgh) presented a new approach, based on recent work [5,6], to the study of radiation reaction by looking at solutions of the Einstein-Maxwell equations in the future null asymptotic region. Introducing a complex worldline identified as the center of mass and charge of the system (which were assumed to coincide), it is found that its equation of motion includes the known radiation-reaction terms. Adam Pound (Guelph) discussed in the first part of his talk how to define adiabatic and radiative approximations to the motion of EMRIs, and what their ambiguities and limitations are. In the second part, using the method of osculating orbits in combination with a two-timescale expansion, he characterized the type of errors that can be produced in the time-dependence of the orbit, in particular in the phase. This was illustrated in test cases of motion under post-Newtonian electromagnetic and gravitational self-forces [7,8]. Larry Price (Gainesville) reviewed recent progress on perturbation theory of a Kerr black hole in relation to the construction of Hertz potentials, discussing the existence of radiation gauges and the question of non-radiated multipoles . Bernard Whiting (Gainesville) continued with this topic and described several tools that can help advancing in this line: GHP formalism tools, separability, symmetry operators, etc. Roland Haas (Guelph) gave the last talk of the day. He presented recent results on the numerical computation, using time-domain techniques, of the scalar self-force on eccentric orbits around a Schwarzschild black hole . The numerical algorithm used is a fourth-order accurate generalization of the characteristic code proposed initially by Lousto and Price. He also presented a generalization of the regularization parameters of the mode-sum regularization scheme to the case of non-geodesic motion.
The third day started with a talk by Carlos Sopuerta (Guelph) on numerical methods in the time-domain for the computation of the gravitational perturbations generated by a particle orbiting a non-rotating black hole. He discussed 1+1 algorithms based on the finite element and the pseudospectral collocation methods, showing results for circular orbits and discussing the prospects for the use of this method in the case of a spinning black hole and calculations of the self-force. Dong-Hoon Kim (Golm) gave a talk on the calculation of the self-force, via the mode-sum scheme, on a particle moving around a slowly rotating black hole. After the break, Bernard Whiting introduced Steve Detweiler (Gainesville) and honored him on the occasion of his 60th birthday, emphasizing the importance of Steve's work not only in the context of the Capra science but in the broader context of General Relativity and its astrophysical applications. In his talk, Steve gave a broad picture of the gravitational self-force effects on orbits around a Schwarzschild black hole. He reminded us about the main issues that need to be tackled: Kerr metric perturbations from the Teukolsky formalism, search for gauge-invariant quantities, second-order perturbations generated by a particle, etc. He also summarized some of the progress already done and presented during the meeting. Jonathan Thornburg (Southampton) gave an introduction to adaptive mesh refinement in double-null coordinates, based on the Berger and Oliger scheme. He discussed the potential applications of this numerical technique to self-force calculations and how it can help reducing their computational cost. The part of the meeting devoted to talks ended with a presentation by Sam Gralla (Chicago) on the locality of the tail integral involved in the calculation of the self-force. His conclusion was that in the general case this integral must be highly non-local.
The rest of the time was allocated for the workshop. The participants were provided with a nice atmosphere to discuss progress and collaborate. In between discussions, and thanks to the generous hospitality of the U.S. Space and Rocket Center and Mr. Cliff Broderick, the organizers and participants enjoyed a very interesting and instructive visit.