We describe the computation of the Bondi news for gravitational radiation. We have implemented a computer code for this problem. We discuss the theory behind it as well as the results of validation tests. Our approach uses the compactified null cone formalism, with the computational domain extending to future null infinity and with a worldtube as inner boundary. We calculate the appropriate full Einstein equations in computational eth form in (a) the interior of the computational domain and (b) on the inner boundary. At future null infinity, we transform the computed data into standard Bondi coordinates and so are able to express the news in terms of its standard N + and N × polarization components. The resulting code is stable and secondorder convergent. It runs successfully even in the highly nonlinear case, and has been tested with the news as high as 400, which represents a gravitational radiation power of about 10 13 M ⊙ /sec.
We generalize the Bondi-Sachs treatment of the initial-value problem using null coordinate systems. This treatment is applicable in both finite and asymptotic regions of space whose sources are bounded by a finite world tube. Using the conformal techniques developed by Penrose, we rederive the results of Bondi and co-workers and of Sachs in conformal-space language. Definitions of asymptotic symmetry "linkages" are developed which offer an invariant way of labeling the properties of finite regions of space, e.g., energy and momentum. These linkages form a representation of the Bondi-Metzner-Sachs asymptotic symmetry group.
We treat the calculation of gravitational radiation using the mixed timelike-null initial value formulation of general relativity. The determination of an exterior radiative solution is based on boundary values on a timelike world tube ⌫ and on characteristic data on an outgoing null cone emanating from an initial cross section of ⌫. We present the details of a three-dimensional computational algorithm which evolves this initial data on a numerical grid, which is compactified to include future null infinity as finite grid points. A code implementing this algorithm is calibrated in the quasispherical regime. We consider the application of this procedure to the extraction of waveforms at infinity from an interior Cauchy evolution, which provides the boundary data on ⌫. This is a first step towards Cauchy-characteristic matching in which the data flow at the boundary ⌫ is two-way, with the Cauchy and characteristic computations providing exact boundary values for each other. We describe strategies for implementing matching and show that for small target error it is much more computationally efficient than alternative methods.
SummaryIn the harmonic description of general relativity, the principle part of Einstein equations reduces to a constrained system of 10 curved space wave equations for the components of the space-time metric. We use the pseudo-differential theory of systems which are strongly well-posed in the generalized sense to establish the well-posedness of constraint preserving boundary conditions for this system when treated in second order differential form. The boundary conditions are of a generalized Sommerfeld type that is benevolent for numerical calculation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.