RIT Logo with Text

Rochester Institute of Technology

Site-wide links

Gravitational Radiation from Binary Black Holes: Advances in the Perturbative Approach
By C O Lousto
Published in Classical Quantum Gravity 22, 15 (Saturday, August 6, 2005)


After the work of Regge, Wheeler, Zerilli, Teukolsky and others in the 1970s, it became possible to accurately compute the gravitational radiation generated by the collision of two black holes (in the extreme-mass limit). It was soon evident that, to first perturbative order, a particle in a circular orbit would continue orbiting forever if the radiative corrections to the particle motion that make the orbit decay were not taken into account. When I entered the field in 1996, a quick search of the literature showed that this problem was still unsolved. A straightforward computation leads to infinities produced by the representation of the particle in terms of Dirac delta functions. Since 1938, when Dirac had solved the equivalent problem in electromagnetic theory, nobody had succeeded in regularizing this in a self-consistent manner. Fortunately, the solution was arrived at much sooner than we expected. In 1997, Mino, Sasaki and Tanaka, and Quinn and Wald published the equations of motion that a particle obeys after self-force corrections. This essentially gave birth to the field of radiation reaction/self-force computations. The aim of this programme is first to obtain the corrections to the geodesic motion of a particle in the background of a single black hole, and then to use this corrected trajectory to compute second-order perturbations of the gravitational field. This will give us the energy-momentum radiated to infinity and into the hole, as well as the waveforms that we will eventually be able to measure with ground- or space-based gravitational wave detectors.

As mentioned, the programme as a whole will give us waveforms accurate to second perturbative order in the mass ratio of the black holes, i.e. Script O[(m/M)2]. This will be a good approximation for galactic binary black holes of the order of a few solar masses, in the right frequency range (few hundred Hertz) to be detected by ground-based gravitational wave interferometers such as LIGO and VIRGO. Other sources of gravitational waves are the product of excitation of the supermassive black holes present in the core of most of the galaxies in the universe by surrounding stars; such a star will eventually get close enough - presumably through three-body encounters - for the gravitational radiation to play an important role in the further evolution of its orbit and eventually cause it to merge into its supermassive companion. As the mass ratios are expected to be of the order of 10-3 at most, our perturbative expansion represents a fantastic degree of accuracy, allowing detailed analysis of the sources by space-based detectors sensitive to sub-Hertz frequencies, such as LISA - a joint mission of NASA and ESA that plans to launch three spaceships in orbit around the sun during the next decade.

The universe can offer us an even more energetic event: when two galaxies collide, the merger of their central supermassive black holes will produce the largest burst of gravitational radiation in the universe. Presumably the mass ratio in this case will be in the range of 1 to 10-3, hence the extreme usefulness of the second-order approach.

Let us return to 1997. After decades of being an open problem, the formulae for the self-force were finally available and, it seemed, ready to be applied in specific computations. This inspired a group of young researchers to meet and study in detail the papers containing the solution to the self-force problem. A ranch donated to Caltech by the movie director Frank Capra made the perfect retreat location, and so in 1998 the series of Capra meetings on radiation reaction was born in San Diego, California. Every year since then, the meeting has incorporated new people and become more formally organized. In 1999 the 2nd Capra meeting took place in Dublin, Ireland1. In 2000 it returned to Caltech2, and in 2001 I had the opportunity to organize the 4th Capra meeting in the Albert Einstein Institute in Germany3. In 2002 Capra 5 was held in Pennsylvania4, and in 2003 the venue for Capra 6 was Kyoto, Japan5. Continuing with the tradition of the meeting taking place in the US on alternate years, I organized the 7th Capra meeting in Brownsville, Texas6 in 2004. This year, the 8th Capra meeting will be in Oxford, UK7.

This volume contains contributions describing the current state of the field and topical areas of interest. It also contains some reviews of the advances made since 1997 and, most interesting to the readers, it describes the open problems and future lines of research in the field. The contributions have been divided into four logical groups. Part I is a collection of papers that deal with first-order perturbation theory. They contain a brief summary of the metric and curvature approaches to perturbations in terms of waveforms and the reconstruction of the metric perturbations in preparation for the computation of the self-force. This section also reviews the energy-momentum balance approach that makes use of the information about the radiation emitted to first perturbative order to correct the trajectory of the particle. Part II comprises works reviewing and expanding the formalism of the self-force. It reviews the newest description in terms of the regular and singular parts of the fields, replacing the original description in terms of tail and divergent parts. Part III contains several examples of application of the self-force formulae, from scalar to gravitational fields and from post-Newtonian expansions to matched expansions. Finally, part IV introduces the problem of computing second-order perturbations of the gravitational field, assuming that we have obtained the corrections to the background geodesic motion of the particle.

We finally call on the next generation of researchers to help complete the radiation reaction programme and further expand it.

CCRG Authors

Lousto, Carlos O.

Research Areas

Binary Black Holes