Related papers: Constraints as evolutionary systems
Rapid growth of constraints is often observed in free evolutions of highly gravitating systems. To alleviate this problem we investigate the effect of adding spatial derivatives of the constraints to the right hand side of the evolution…
The Einstein evolution equations are studied in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasilinear elliptic--hyperbolic system of evolution…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
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…
The goal of this work was to investigate the propagation of the constraints in the ghost-free bimetric theory where the evolution equations are in standard 3+1 form. It is established that the constraints evolve according to a first-order…
In the Cauchy problem of general relativity one considers initial data that satisfies certain constraints. The evolution equations guarantee that the evolved variables will satisfy the constraints at later instants of time. This is only…
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…
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 consider a periodic evolution inclusion defined on an evolution triple of spaces. The inclusion involves also a subdifferential term. We prove existence theorems for both the convex and the nonconvex problem, and we also produce extremal…
We solve the Einstein constraint equations for a 3 + 1 dimensional vacuum spacetime with a space-like translational Killing field in the asymptotically flat case.. The presence of a space-like translational Killing field allows for a…
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…
Systems of PDEs comprised of a combination of constraints and evolution equations are ubiquitous in physics. For both theoretical and practical reasons, such as numerical integration, it is desirable to have a systematic understanding of…
We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and…
Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are…
It is possible to solve the Einstein constraint equations as an evolutionary rather than an elliptic system. Here we consider the Gauss constraint in electrodynamics as a toy model for thist. We use a combination of the evolutionary method…
The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A new formulation of constraint-preserving boundary conditions of…
We review some well posed formulations of the evolution part of the Cauchy problem of General Relativity that we have recently obtained. We include also a new first order symmetric hyperbolic system based directly on the Riemann tensor and…
We discuss the problem of non abelian constrained systems and the origin of appearance of non abelian algebras. We show that it is possible, in principle, to change a non abelian system to an abelian one, at least locally. Our method is…
We show that the 3+1 vacuum Einstein field equations in Ashtekar's variables constitutes a first order symmetric hyperbolic system for arbitrary but fixed lapse and shift fields, by suitable adding to the system terms proportional to the…
We use an orthonormal frame approach to provide a general framework for the first order hyperbolic reduction of the Einstein equations coupled to a fairly generic class of matter models. Our analysis covers the special cases of dust and…