The overlap of numerical relativity, perturbation theory and post-Newtonian theory in the binary black hole problem

Inspiralling and coalescing binary black holes are promising sources of gravitational radiation. The orbital motion and gravitational-wave emission of such system can be modeled using a variety of approximation schemes and numerical methods in general relativity: The post-Newtonian (PN) formalism, black hole perturbation theory (BHP), numerical relativity (NR) simulations and the effective one-body (EOB) model. We review recent work at the multiple interfaces of these analytical and numerical techniques, emphasizing the use of coordinate-invariant relationships to perform meaningful comparisons. Such comparisons provide independent checks of the validity of the various calculations, they inform the development of a universal, semi-analytical model of the binary dynamics and gravitational-wave emission and they help to delineate the respective domains of validity of each approximation method. For instance, several recent comparisons suggest that perturbation theory may find applications in a broader range of physical problems than previously thought, including the radiative inspiral of intermediate mass-ratio and comparable-mass black hole binaries.