7.1 Synergism between perturbation theory and numerical relativity

Fifteen years ago with the advancements in computer power, we could not think that perturbation theory would continue to play such an important role in many problems. Today it is widely accepted that there is a need for the development of new approximation schemes to accompany large scale simulations. Fully relativistic computer simulations give only numerical answers to problems; often these answers do not provide physical understanding of which principles are important, or even what principles govern a given process. Even more, in some cases, simulation results can be simply incorrect or misleading. By closely coupling various perturbation schemes it is possible to interpret and confirm simulation results.

For example, during the late stages of black hole or stellar coalescence or supernovae collapse, the system settles down to a slightly perturbed black hole or neutron star. Numerical codes, evolving the full nonlinear Einstein equations, should be able to accurately compute the waveforms required for gravitational wave detection. Parallel to this, it should be possible to evolve the perturbations of both black holes and stars (governed by their own linear evolution equations) for the same set of initial data. This is an important check of the fully nonlinear codes. An excellent example is the head-on collision of two black holes. This sounds like an impossible task for perturbation theory but it can be achieved if the two black holes are close together and they can be considered as having already merged into a single perturbed black hole (close limit); see more details in a recent review by Pullin [172]. Much work has already been performed for head-on collisions of two non-rotating black holes but the more realistic problem for the inspiral collision of rotating black holes is still open.

Following in the same spirit are more recent calculations [5] of the close limit for two identical neutron stars. The results show the excitation of stellar QNMs and it remains for numerical relativity to verify the results.

Finally, perturbation theory can be also used as a tool to construct a gauge invariant measure of the gravitational radiation in a numerically generated perturbed black hole spacetime [7184].

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