The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem

TL;DR

This paper reviews how different approximation and numerical methods in general relativity are compared and integrated to improve modeling of binary black hole systems and gravitational wave predictions.

Contribution

It highlights recent efforts to compare and combine post-Newtonian, perturbation, and numerical relativity techniques for better binary black hole modeling.

Findings

Perturbation theory may be applicable to a wider range of binary systems.

Coordinate-invariant relationships enable meaningful comparisons between methods.

Comparisons help define the validity domains of each approximation.

Abstract

Inspiralling and coalescing binary black holes are promising sources of gravitational radiation. The orbital motion and gravitational-wave emission of such system can be modelled using a variety of approximation schemes and numerical methods in general relativity: the post-Newtonian formalism, black hole perturbation theory, numerical relativity simulations, and the effective one-body 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.