The Lazarus Project

Black holes are the most interesting and extraordinary objects predicted by Einstein's general relativity. No longer regarded as science fiction, black holes are now expected to be rather common astrophysical objects, occurring even in pairs. There is increasing astronomical evidence of black hole binaries in many galaxies, formed long before by the collapse of huge amounts of matter. Some interesting simulations indicate that these systems may also be commonly generated in globular clusters.

Binary black hole systems orbiting around one another are particularly interesting because they lose energy due to emission of gravitational radiation, spiral inwards, and eventually merge into a single remnant black hole almost twice the size. The violence of the collision whips space itself into wild vibrations. These gravitational waves race outwards from the collision with the speed of light, carrying huge amounts of energy. Starting in 2002, a new generation of gravitational wave detectors (e.g. LIGO, GEO, VIRGO etc) hopes to catch these waves. Many astronomers believe that the first waves caught will be from merging black holes.

On the theoretical side the study of binary black hole mergers is now one of the most exciting and challenging topics in the astrophysical relativity community. Several theoretical approaches have been developed for treating these systems. The post-Newtonian approximation has provided a good understanding of the early slow adiabatic inspiral phase of these systems, applicable when the black holes are not too close, in what we may call the ``far limit''. Likewise, the ``close limit'' approximation, black hole perturbation theory, can successfully describe the system at late times when it is dynamically similar to a single black hole, which ``rings-down'' as it radiates away its distortions. Between these stages, when the system is near the ``innermost stable circular orbit'', orbital inspiral dynamics are expected to give way to a rapid plunge and coalescence. Here the two-body dynamics are most significant, obstructing any approximation method, and the system can be treated only by a fully non-linear numerical simulation of Einstein's gravitational field equations.

Intensive efforts have been underway in the past decade to write numerical codes able to solve Einstein's system of ten coupled non-linear partial differential equations, on powerful supercomputers. In the U.S., this effort was primarily undertaken by a Grand Challenge collaboration and then continued in a number of groups, but so far the numerical treatment of black hole systems in full 3D has proved very difficult. Motivated by the desire to provide expectant gravitational wave observers with some long-awaited estimate of the full merger waveforms, and to prepare the arena for future, more advanced numerical simulations, we have recently pursued a hybrid approach to the problem, called the Lazarus project. The underlying idea of the Lazarus project is very simple: apply the ``far limit'', full numerical and close limit treatments in sequence. In this way we can shift the finite time interval of full non-linear numerical evolution to cover the stage of the dynamics where no perturbative approach is applicable, and still derive the complete black hole ring-down and the propagation of radiation into the wave zone with a close limit perturbative treatment. The perturbative model not only allows an inexpensive and stable continuation of the evolution (which is then allowed to rise and live again like the biblical Lazarus), but also supplies a clear interpretation of the dynamics not manifest in the generic numerical simulation. Last year, we successfully addressed the problem of combining the close-limit approximation describing ringing black holes and full numerical relativity, required for essentially nonlinear interactions, producing the first calculation of complete plunge waveforms, total gravitational energy, angular momentum radiated from the coalescence of two black holes from an estimate of the innermost stable circular orbit down to the final single rotating black hole. 

Our work has been featured in the News and Views section of Nature (see the picture story ). Our latest results were used to improve an astrophysical model in a groundbreaking article to appear soon in Science on radio-jet evidence for supermassive black holes.

Our next goal is to refine our approach and working together with several colleagues in the numerical relativity group to extend the duration of the numerical simulations to permit studies of more separated black hole configurations. The reason is that we would like to build a connection to more astrophysically realistic initial data descriptions such as with a true interface to the post-Newtonian approximation. We are also particularly interested in using the machinery of the Lazarus project as a tool to improve detection strategies for black hole collision waveforms (the Kudu project). The first step will be to explore the dependence of the waveforms on the astrophysical parameters, such as mass ratios and spin magnitudes and orientation, for binary black hole binary systems. For more information, please see: 
  • Original paper: Plunge Waveforms from Inspiralling Binary Black Holes
    J. Baker, B. Brügmann, M. Campanelli, C. O. Lousto, and R. Takahashi 
    Physical Review Letters 17 September 2001 (Published 31 August 2001) 
  • Detailed Theory Paper: The Lazarus project: A pragmatic approach to binary black hole evolution
    Baker, J and Campanelli, M and Lousto, C O
    Physical Review D (2002) pp. 044001, 
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Last update October 31, 2005

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