Towards a wave--extraction method for numerical relativity: III. Analytical examples for the Beetle--Burko radiation scalar

摘要

Beetle and Burko recently introduced a background--independent scalarcurvature invariant for general relativity that carries information only aboutthe gravitational radiation in generic spacetimes, in cases where suchradiation is incontrovertibly defined. In this paper we adopt a formalism thatonly uses spatial data as they are used in numerical relativity and compute theBeetle--Burko radiation scalar for a number of analytical examples,specifically linearized Einstein--Rosen cylindrical waves, linearizedquadrupole waves, the Kerr spacetime, Bowen--York initial data, and the Kasnerspacetime. These examples illustrate how the Beetle--Burko radiation scalar canbe used to examine the gravitational wave content of numerically generatedspacetimes, and how it may provide a useful diagnostic for initial data sets.