Extraction of gravitational waves in numerical relativity

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.

Parameter estimation method that directly compares gravitational wave observations to numerical relativity

“…While gravitational waves are defined at null infinity, the finite size of typical NR computational domains implies that a computational technique must identify the appropriate asymptotic radiation from the simulation [25]. This method generally has error, often associated with systematic neglect of near-field physics in the asymptotic expansion used to extract the wave (i.e., truncation error).…”

Taub-NUT from the Dirac monopole

“…Asymptotically flat spacetimes have been extensively studied over the last 50 years, particularly, recently, in the context of gravitational wave detections [1] and asymptotic symmetry groups [2,3]. In this paper, motivated by recent work on dual gravitational charges [4][5][6][7], we show how treating asymptotically flat spacetimes in terms of a characteristic value problem [8] provides an intriguing way of viewing the Dirac magnetic monopole as a progenitor of the Taub-NUT spacetime.…”

“…In this paper, motivated by recent work on dual gravitational charges [4][5][6][7], we show how treating asymptotically flat spacetimes in terms of a characteristic value problem [8] provides an intriguing way of viewing the Dirac magnetic monopole as a progenitor of the Taub-NUT spacetime. 1 Our starting point is to consider a general class of asymptotically flat metrics, written in a Bondi coordinate system (u, r, x I = {θ, φ}), such that the metric takes the form 2…”

Spin coefficients and gauge fixing in the Newman-Penrose formalism

“…In 1973 Teukolsky [3] formulated his famous master equation based on the NP formalism giving decoupled perturbation equations for two Weyl scalars Ψ 0 and Ψ 4 . This strengthened the idea of these scalar fields being associated with the gravitational waves degrees of freedom, respectively ingoing and outgoing, a result that had been already anticipated by Newman and Penrose in their seminal paper.With the advent of numerical relativity the NP formalism found another important application: a tool for gravitational wave extraction in numerical simulations (for an exhaustive review on wave extraction methods see [4]). Given its tight association to the gravitational wave degrees of freedom and its coordinate invariant properties, the calculation of Ψ 4 in a numerical grid seemed to be the most natural candidate for a rigorous wave extraction methodology.…”

“…With the advent of numerical relativity the NP formalism found another important application: a tool for gravitational wave extraction in numerical simulations (for an exhaustive review on wave extraction methods see [4]). Given its tight association to the gravitational wave degrees of freedom and its coordinate invariant properties, the calculation of Ψ 4 in a numerical grid seemed to be the most natural candidate for a rigorous wave extraction methodology.…”