Second Capra workshop on Black Holes

and Gravitational Waves

Patrick R Brady, University of Wisconsin-Milwaukee
Alan G Wiseman, University of Wisconsin-Milwaukee

An informal workshop took place at University College Dublin, Ireland from 16-20 August 1999. The workshop emphasized theoretical methods to investigate gravitational-wave generation, implications of gravitational-wave astronomy for theorists, and identification of important open problems.

There were 18 participants at the workshop. During the first three days, there were 12 talks by participants. Each talk was 30-50 minutes in duration followed by equal time for discussion. An outing to nearby Powerscourt and Glendalough was organized for Thursday. Friday morning was devoted to informal presentations by the remaining participants. The workshop was a huge success; it was generally agreed that the format made for an excellent atmosphere to share and discuss the many results that were presented.

Steve Detweiler made the first presentation. His work (in collaboration with Lee Brown) uses a Regge-Wheeler formalism to compute the $O(\mu/M)$ corrections to geodesic motion for a particle orbiting a Schwarzschild black hole. He presented preliminary results which indicate that the orbital frequency is reduced at the innermost stable circular orbit when compared to the test particle limit. Detweiler's talk set the tone for the workshop by reporting new results from work in progress, and by encouraging open discussion of the material.

Scott Hughes reported on progress computing the effects of radiation reaction without the use of radiation reaction forces. He showed results for the radiative evolution of orbits and gravitational waveforms generated by small objects in circular, non-equatorial orbits around Kerr black holes. Perhaps the most interesting result is that the tilt angle of inclined orbits changes extremely slowly -- more slowly in the strong-field than would be predicted by post-Newtonian theory.

Kostas Glempedakis and Sathyaprakash reported on work in progress at Cardiff. Kostas discussed ongoing work on radiation reaction effects. Sathya discussed the P-approximants: a class of approximate waveforms that model gravitational waves from inspiralling and coalescing compact binaries. The waveforms are constructed using two inputs: (a) two new energy-type and flux-type functions and (b) the systematic use of Padé approximation for constructing successive approximants of these new functions. The new P-approximants have larger overlaps and smaller biases than the standard Taylor-series approximants. They also converge faster and monotonically. The presently available $\left (v/c\right )^5$-accurate post-Newtonian results can be used to construct P-approximate waveforms that provide overlaps with the ``exact'' waveform larger than $96.5\%,$ implying that more than 90% of potential events can be detected with the aid of P-approximants as opposed to a mere 50% that would be detectable using standard post-Newtonian approximants.

Alan Wiseman discussed methods of computing the instantaneous radiation reaction force on scalar charges orbiting Schwarzschild black holes. These calculations utilize the DeWitt-Brehme method of regularization, where the force is computed from the ``tail'' of the Green's function. He also reported on progress computing the forces both from the mode sum of the Green's function and analytic expressions for the Green's function.

Amos Ori followed Wiseman by presenting a concrete a method of computing the radiation reaction force with a mode sum. Although the contribution of each individual $l,m,\omega$ mode to the self-force is finite, the naive sum of these contributions generically diverges (for certain components of the force). Amos presented a new method for regularizing the mode sum. In this method the mode-sum procedure is modified in a suitable way, in order to obtain the correct (and finite) expression for the self-force.

Lior Burko presented simple, though non-trivial, applications of Ori's prescription for mode-sum regularization of self forces. For the cases of static scalar or electric charges in Schwarzschild spacetime, Burko's calculations recover the results known from completely different procedures. Burko also presented results for the self force acting on a scalar charge in circular motion around a Schwarzschild black hole in the strong field regime. The conservative self-force is attractive, and scales like the black hole's mass squared.

Warren Anderson discussed work in progress with Éanna Flanagan. They use dimensional and counting arguments to calculate the contribution to the gravitational radiation reaction force from the normal neighborhood of a massive particle in an arbitrary vacuum spacetime. Their method involves expansions in (geodetic distance)/(radius of curvature) and (particle mass)/(radius of curvature).

Brian Nolan spoke about two subjects. He reported on work on the strength of the central singularity in spherical gravitational collapse. He also gave a brief critical review of attempts to define black holes in arbitrary spacetimes using surfaces foliated by marginally trapped 2-surfaces.

Eric Poisson reported on his own calculation of the Price power-law decay of radiative fields (scalar, electromagnetic, and gravitational) in Schwarzschild spacetime. His approach has the advantage of linking the behavior of the field at future null infinity and near future timelike infinity in a natural way: The two different power indices arise by taking two different limits of a single expression. His method also yields the field's behavior on the event horizon, complete with all multiplicative factors.

Éanna Flanagan talked about the non-detectability of squeezed statistical properties of relic gravitational waves from the early Universe, based on work with Allen and Papa (gr-qc/9906054). He reported, contrary to a claim of Grishchuk (gr-qc/9810055), that even if relic gravitational waves are detected by LIGO/VIRGO or LISA, their squeezed nature will not be detectable. The squeezing is only detectable by experiments whose duration is comparable to the age of the Universe at the time of measurement. The analysis does not rule out indirect detections of the squeezing via measurements of the CMBR, since CMBR photons measure the stochastic background over a time comparable to the age of the Universe at recombination.

Nils Anderson presented recent results concerning the late-time behavior of perturbations in the Kerr geometry. He discussed analytic calculations based on the contribution from the black hole's virtually undamped quasinormal modes that indicated that the field would oscillate with an amplitude that falls of inversely with time (much slower that the familiar power-law tails). The analytic work was supported by numerical evolutions using the scalar field Teukolsky code. He suggested that this is a new (superradiance related) phenomenon in black hole physics.

During a spectacular day in the Wicklow countryside on Thursday, discussion continued on the many aspects of modeling gravitational wave generation from astrophysical systems. At the final session on Friday morning, Dan Kennefick gave a short report on his recent work studying the sociology of the community of theorists working on gravitational waves. The presentation was received with keen interest by the audience, some of whom had participated in one of the issues discussed by Dan. Jolien Creighton discussed an approach to identifying the gauge invariant component of the work done by tidal forces in a binary system. In a short presentation, Patrick Brady suggested that the Kerr-Schild form of black hole spacetimes might be useful when computing approximate expressions for the radiation reaction force on objects orbiting black holes. Finally, Ben Owen discussed the relevance of gravitational radiation reaction for the r-modes of nascent neutron stars.

In conclusion, Adrian Ottewill's excellent organization contributed significantly to the success of the second Capra workshop on gravitational waves. The workshop was wonderfully paced and organized, allowing a great degree of participation by everyone. An atmosphere of lively debate was facilitated by the allotment of equal time for talks and discussion.

And yes, ``Capra'' does refer to Frank Capra, the American movie director. Frank Capra was a Caltech alumnus and benefactor. The first ``Capra'' workshop took place last summer at his ranch outside of Los Angeles.

The workshop was supported in part by funds from University College Dublin. More information can be found at

Jorge Pullin