Related papers: Exact boundary conditions in numerical relativity …

In this work, we present a work in progress towards an efficient and economical computational module which interfaces between Cauchy and characteristic evolution codes. Our goal is to provide a standardized waveform extraction tool for the…

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately…

A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon system with spherical symmetry is presented. Initial data are specified on the union of a space-like and null hypersurface. The development of the data is obtained…

We present gauge invariant spectral Cauchy characteristic extraction. We compare gravitational waveforms extracted from a head-on black hole merger simulated in two different gauges by two different codes. We show rapid convergence,…

We extract gravitational waveforms from numerical simulations of black hole binaries computed using the Spectral Einstein Code. We compare two extraction methods: direct construction of the Newman-Penrose (NP) scalar $\Psi_4$ at a finite…

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to current 3D black codes that simulate…

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…

We present a new approach for the Cauchy-characteristic extraction of gravitational radiation strain, news function, and the flux of the energy-momentum, supermomentum and angular momentum associated with the Bondi-Metzner-Sachs asymptotic…

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 present a spectral algorithm for solving the full nonlinear vacuum Einstein field equations in the Bondi framework. Developed within the Spectral Einstein Code (SpEC), we demonstrate spectral characteristic evolution as a technical…

We develop and calibrate a characteristic waveform extraction tool whose major improvements and corrections of prior versions allow satisfaction of the accuracy standards required for advanced LIGO data analysis. The extraction tool uses a…

This is the first paper in a series aimed to implement boundary conditions consistent with the constraints' propagation in 3D numerical relativity. Here we consider spherically symmetric black hole spacetimes in vacuum or with a minimally…

We develop a numerical method suitable for gravitational collapse based on Cauchy evolution with an ingoing characteristic boundary. Unlike similar methods proposed recently (Ripley; Bieri, Garfinkle & Yau 2019/20), the numerical grid…

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…

We investigate the interior of a dynamical black hole as described by the Einstein-Maxwell-charged-Klein-Gordon system of equations with a cosmological constant, under spherical symmetry. In particular, we consider a characteristic initial…

Causal differencing has shown to be one of the promising and successful approaches towards excising curvature singularities from numerical simulations of black hole spacetimes. So far it has only been actively implemented in the ADM and…

This paper studies the Cauchy problem for systems of semi-linear wave equations on $\mathbb{R}^{3+1}$ with nonlinear terms satisfying the null conditions. We construct future global-in-time classical solutions with arbitrarily large initial…

In this thesis the universal collapse of vacuum Brill waves is demonstrated numerically and analytically. This thesis presents the mathematical and numerical methods necessary to regularise and evolve Brill Gravitational Waves in spherical…

Although the traditional form of the Einstein field equations is intrinsically four-dimensional, the field of numerical general relativity focuses on the reformulation of these equations as a 3 + 1-dimensional Cauchy problem, in which…

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…