Related papers: Einstein-Klein-Gordon system via Cauchy-characteri…
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…
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…
This paper gives a detailed pedagogic presentation of the central concepts underlying a new algorithm for the numerical solution of Einstein's equations for gravitation. This approach incorporates the best features of the two leading…
We present the first numerical relativity waveforms for binary black hole mergers produced using spectral methods that show both the displacement and the spin memory effects. Explicitly, we use the SXS Collaboration's $\texttt{SpEC}$ code…
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 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…
In representation learning, Convolutional Sparse Coding (CSC) enables unsupervised learning of features by jointly optimising both an \(\ell_2\)-norm fidelity term and a sparsity enforcing penalty. This work investigates using a…
We present a detailed methodology for extracting the full set of Newman-Penrose Weyl scalars from numerically generated spacetimes without requiring a tetrad that is completely orthonormal or perfectly aligned to the principal null…
We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the…
We study the nonlinear stability of the Cauchy horizon in the interior of extremal Reissner-Nordstr\"om black holes under spherical symmetry. We consider the Einstein-Maxwell-Klein-Gordon system such that the charge of the scalar field is…
Global properties of maximal future Cauchy developments of stationary, m-dimensional asymptotically flat initial data with an outer trapped boundary are analyzed. We prove that, whenever the matter model is well posed and satisfies the null…
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…
Spherically symmetric, time-periodic oscillatons -- solutions of the Einstein-Klein-Gordon system (a massive scalar field coupled to gravity) with a spatially localized core -- are investigated by very precise numerical techniques based on…
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…
The late-time behavior of a scalar field on fixed Kerr background is examined in a numerical framework incorporating the techniques of conformal compactification and hyperbolic initial value formulation. The applied code is 1+(1+2) as it is…
We study the initial value problem in Einstein-Cartan theory which includes torsion and, therefore, a non-symmetric connection on the spacetime manifold. Generalizing the path of a classical theorem by Choquet-Bruhat and York for the…
The details are presented of a new evolution algorithm for the characteristic initial-boundary value problem based upon an affine parameter rather than the areal radial coordinate used in the Bondi-Sachs formulation. The advantages over the…
Motivated by the goal for high accuracy modeling of gravitational radiation emitted by isolated systems, recently, there has been renewed interest in the numerical solution of the hyperboloidal initial value problem for Einstein's field…
In numerical computations of Einstein's equations for black hole spacetimes, it will be necessary to use approximate boundary conditions at a finite distance from the holes. We point out here that ``tails,'' the inverse power-law decrease…