相关论文: Three Dimensional Numerical Relativity with a Hype…
We discuss several explicitly causal hyperbolic formulations of Einstein's dynamical 3+1 equations in a coherent way, emphasizing throughout the fundamental role of the ``slicing function,'' $\alpha$---the quantity that relates the lapse…
This paper presents both a numerical method for general relativity and an application of that method. The method involves the use of harmonic coordinates in a 3+1 code to evolve the Einstein equations with scalar field matter. In such…
$3+1$ formulations of the Einstein field equations have become an invaluable tool in Numerical relativity, having been used successfully in modeling spacetimes of black hole collisions, stellar collapse and other complex systems. It is…
A code that implements Einstein equations in the characteristic formulation in 3D has been developed and thoroughly tested for the vacuum case. Here, we describe how to incorporate matter, in the form of a perfect fluid, into the code. The…
We report on our numerical implementation of fully relativistic hydrodynamics coupled to Einstein's field equations in three spatial dimensions. We briefly review several steps in our code development, including our recasting of Einstein's…
I review recent developments in numerical relativity, focussing on progress made in 3D black hole evolution. Progress in development of black hole initial data, apparent horizon boundary conditions, adaptive mesh refinement, and…
We present a new numerical code designed to solve the Einstein field equations for axisymmetric spacetimes. The long term goal of this project is to construct a code that will be capable of studying many problems of interest in axisymmetry,…
We present a new formulation of the Einstein equations that casts them in an explicitly first order, flux-conservative, hyperbolic form. We show that this now can be done for a wide class of time slicing conditions, including maximal…
We find a choice of variables for the 3+1 formulation of general relativity which casts the evolution equations into (flux-conservative) symmetric-hyperbolic first order form for arbitrary lapse and shift, for the first time. We redefine…
The effectiveness of the hyperbolic relaxation method for solving the Einstein constraint equations numerically is studied here on a variety of compact orientable three-manifolds. Convergent numerical solutions are found using this method…
We investigate a class of cosmological solutions of Einstein's field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject…
We study the stability of three-dimensional numerical evolutions of the Einstein equations, comparing the standard ADM formulation to variations on a family of formulations that separate out the conformal and traceless parts of the system.…
New numerical methods have been applied in relativity to obtain a numerical evolution of Einstein equations much more robust and stable. Starting from 3+1 formalism and with the evolution equations written as a FOFCH (first-order flux…
We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on…
We show that the Kidder-Scheel-Teukolsky family of hyperbolic formulations of the 3+1 evolution equations of general relativity remains hyperbolic when coupled to a recently proposed modified version of the Bona-Masso slicing condition.
The article presents some aspects concerning the construction of a new thorn for the Cactus code, a complete 3-dimensional machinery for numerical relativity. This thorn is completely dedicated to numerical simulations in cosmology, that…
Recent years have seen a significant progress in the development of general relativistic codes for the numerical solution of the equations of magnetohydrodynamics in spacetimes with high and dynamical curvature. These codes are valuable…
A general covariant extension of Einstein\'{}s field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector $Z_\mu$. Einstein's solutions…
We prove a global well-posedness and asymptotic convergence theorem for the \((3+1)\)-dimensional vacuum Einstein equations with positive cosmological constant \(\Lambda\) on globally hyperbolic spacetimes \(\widetilde M \cong M \times…
We present a new many-parameter family of hyperbolic representations of Einstein's equations, which we obtain by a straightforward generalization of previously known systems. We solve the resulting evolution equations numerically for a…