Related papers: First order hyperbolic formalism for Numerical Rel…
In this work, we study of the algebraic-hyperbolic formulation of the Einstein constraint equations for numerically constructing initial data sets for inhomogeneous cosmological space-times with $\mathbb{T}^3$ topology. We implement a…
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…
With the aim of deriving symmetric hyperbolic free-evolution systems for GR that possess Hamiltonian structure and allow for the popular puncture gauge condition we analyze the hyperbolicity of Hamiltonian systems. We develop helpful tools…
We consider an approach to the hyperboloidal evolution problem based on the Einstein equations written for a rescaled metric. It is shown that a conformal scale factor can be freely prescribed a priori in terms of coordinates in a…
The integration of the Einstein equations split into the solution of constraints on an initial space like 3 - manifold, an essentially elliptic system, and a system which will describe the dynamical evolution, modulo a choice of gauge. We…
Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint…
We study properties of evolution equations which are first order in time and arbitrary order in space (FTNS). Following Gundlach and Mart\'in-Garc\'ia (2006) we define strong and symmetric hyperbolicity for FTNS systems and examine the…
Motivated by the need to control the exponential growth of constraint violations in numerical solutions of the Einstein evolution equations, two methods are studied here for controlling this growth in general hyperbolic evolution systems.…
The generalized harmonic representation of Einstein's equation is manifestly hyperbolic for a large class of gauge conditions. Unfortunately most of the useful gauges developed over the past several decades by the numerical relativity…
Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…
We establish a variant, which has the advantage of introducing only physical characteristics, of the symmetric quasi linear first order system given by H.\ Friedrich for the evolution equations of gravitating fluid bodies in General…
We discuss a successful three-dimensional cartesian implementation of the Bona-Mass\'o hyperbolic formulation of the 3+1 Einstein evolution equations in numerical relativity. The numerical code, which we call ``Cactus,'' provides a general…
We consider two strongly hyperbolic Hamiltonian formulations of general relativity and their numerical integration with a free and a partially constrained symplectic integrator. In those formulations we use hyperbolic drivers for the shift…
We derive a new first-order formulation for Einstein's equations which involves fewer unknowns than other first-order formulations that have been proposed. The new formulation is based on the 3+1 decomposition with arbitrary lapse and…
The Einstein equations have proven surprisingly difficult to solve numerically. A standard diagnostic of the problems which plague the field is the failure of computational schemes to satisfy the constraints, which are known to be…
The Einstein evolution equations may be written in a variety of equivalent analytical forms, but numerical solutions of these different formulations display a wide range of growth rates for constraint violations. For symmetric hyperbolic…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
A new constraint suppressing formulation of the Einstein evolution equations is presented, generalizing the five-parameter first-order system due to Kidder, Scheel and Teukolsky (KST). The auxiliary fields, introduced to make the KST system…
A possible definition of strong/symmetric hyperbolicity for a second-order system of evolution equations is that it admits a reduction to first order which is strongly/symmetric hyperbolic. We investigate the general system that admits a…
We investigate the well-posedness of the characteristic initial-boundary value problem for the Einstein equations in Bondi-like coordinates (including Bondi, double-null and affine). We propose a definition of strong hyperbolicity of a…