Related papers: Cauchy-perturbative matching and outer boundary co…

We present a new method of extracting gravitational radiation from three-dimensional numerical relativity codes and providing outer boundary conditions. Our approach matches the solution of a Cauchy evolution of Einstein's equations to a…

We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as…

Computational techniques which establish the stability of an evolution-boundary algorithm for a model wave equation with shift are incorporated into a well-posed version of the initial-boundary value problem for gravitational theory in…

We investigate the numerical stability of Cauchy evolution of linearized gravitational theory in a 3-dimensional bounded domain. Criteria of robust stability are proposed, developed into a testbed and used to study various…

This thesis describes the application of numerical techniques to solve Einstein's field equations in three distinct cases. First we present the first long-term stable second order convergent Cauchy characteristic matching code in…

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 worldtube…

Gravitational waves provide a powerful enhancement to our understanding of fundamental physics. To make the most of their detection we need to accurately model the entire process of their emission and propagation toward interferometers.…

From Einstein's theory we know that besides the electromagnetic spectrum, objects like quasars, active galactic nuclei, pulsars and black holes also generate a physical signal of purely gravitational nature. The actual form of the signal is…

I describe a new algorithm for solving nonlinear wave equations. In this approach, evolution takes place on characteristic hypersurfaces. The algorithm is directly applicable to electromagnetic, Yang-Mills and gravitational fields and other…

We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a…

Cauchy-Characteristic Matching (CCM), the combination of a central 3+1 Cauchy code with an exterior characteristic code connected across a time-like interface, is a promising technique for the generation and extraction of gravitational…

We present a framework to propagate to null infinity gravitational waves computed at timelike worldtubes in the interior of a 3+1 (Cauchy) numerical relativity simulations. In our method, numerical relativity data are used as the inner…

We implement a code to find the gravitational news at future null infinity by using data from a Cauchy code as boundary data for a characteristic code. This technique of Cauchy-characteristic Extraction (CCE) allows for the unambiguous…

An outstanding issue in the treatment of boundaries in general relativity is the lack of a local geometric interpretation of the necessary boundary data. For the Cauchy problem, the initial data is supplied by the 3-metric and extrinsic…

We present an improved spectral algorithm for Cauchy-characteristic extraction and characteristic evolution of gravitational waves in numerical relativity. The new algorithms improve spectral convergence both at the poles of the…

We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic…

We present several improvements to the Cauchy-characteristic evolution procedure that generates high-fidelity gravitational waveforms at $\mathcal{I}^+$ from numerical relativity simulations. Cauchy-characteristic evolution combines an…

The accurate modeling of gravitational radiation is a key issue for gravitational wave astronomy. As simulation codes reach higher accuracy, systematic errors inherent in current numerical relativity wave-extraction methods become evident,…

The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…

We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative…