Abstract
A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at null infinity and in an appropriate coordinate system, the accurate estimation of the emitted gravitational waves represents an old and non-trivial problem in numerical relativity. A number of methods have been developed over the years to “extract” the radiative part of the solution from a numerical simulation and these include: quadrupole formulas, gauge-invariant metric perturbations, Weyl scalars, and characteristic extraction. We review and discuss each method, in terms of both its theoretical background as well as its implementation. Finally, we provide a brief comparison of the various methods in terms of their inherent advantages and disadvantages.Electronic supplementary materialThe online version of this article (doi:10.1007/s41114-016-0001-9) contains supplementary material, which is available to authorized users.
Highlights
With the commissioning of the second generation of laser interferometric gravitationalwave detectors, and the recent detection of gravitational waves (Abbott 2016), there is considerable interest in gravitational-wave astronomy
The key difficulty is that gravitational waves are unambiguously defined only at future null infinity (J +), whereas in practice the domain of numerical simulations is a region of finite extent using a “3+1” foliation of the spacetime
The relative difference in amplitude was of 50 % at most, which is probably acceptable given that these formulas are usually employed in complex astrophysical calculations in which the systematic errors coming from the microphysical modelling are often much larger
Summary
With the commissioning of the second generation of laser interferometric gravitationalwave detectors, and the recent detection of gravitational waves (Abbott 2016), there is considerable interest in gravitational-wave astronomy This is a huge field, covering the diverse topics of: detector hardware construction and design; data analysis; astrophysical source modeling; approximate methods for gravitational-wave calculation; and, when the weak field approach is not valid, numerical relativity. The key difficulty is that gravitational waves are unambiguously defined only at future null infinity (J +), whereas in practice the domain of numerical simulations is a region of finite extent using a “3+1” foliation of the spacetime. This is true for most of the numerical codes, but there are notable exceptions. These attempts include the hyperboloidal method (Frauendiener 2004), Cauchy characteristic matching (Winicour 2005), and
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