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Numerical Relativity at UT Brownsville

The Lazarus Project

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; 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 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 Lazarus is very simple (see Figure): apply the far-limit (FL), full-numerical (FN) and close-limit (CL) treatments in sequence. In this way we can restrict the finite time interval of full non-linear numerical evolution to covering 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. Lazarus picture
We have 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 in a groundbreaking article in Science to improve an astrophysical model on radio-jet evidence for supermassive black holes.

Future Directions

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 black-hole binary systems.

We are working on extending Lazarus by using the quasi-Kinnersley tetrad. The resulting Lazarus 2 will be more robust than original Lazarus.

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