Related papers: Constraint-preserving Sommerfeld conditions for th…
This is the first of a series of papers describing a numerical implementation of the conformally rescaled Einstein equation, an implementation designed to calculate asymptotically flat spacetimes, especially spacetimes containing black…
A contradiction arises when applying standard boundary conditions to a simple quantum rotator with a single coordinate. New boundary conditions for the Schroedinger equation are proposed that involve only gauge invariant quantities, and…
The dynamics of classical field theories is usually governed by field equations, but when fields are constrained to bounded domains it is also dependent on its boundary conditions. Usually boundary conditions are constrained by the…
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…
Via the AdS/CFT correspondence, fundamental constraints on the entanglement structure of quantum systems translate to constraints on spacetime geometries that must be satisfied in any consistent theory of quantum gravity. In this paper, we…
We consider the Helmholtz equation defined in unbounded domains, external to 2D bounded ones, endowed with a Dirichlet condition on the boundary and the Sommerfeld radiation condition at infinity. To solve it, we reduce the infinite region,…
In "extended phase space" approach to quantum geometrodynamics numerical solutions to Schrodinger equation corresponding to various choice of gauge conditions are obtained for the simplest isotropic model. The "extended phase space"…
We study generalisations of the Einstein--Straus model in cylindrically symmetric settings by considering the matching of a static space-time to a non-static spatially homogeneous space-time, preserving the symmetry. We find that such…
We prove localized energy estimates for the wave equation in domains with a strictly concave boundary when homogeneous Dirichlet or Neumann conditions are imposed. By restricting the solution to small, frequency dependent, space time…
The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…
This paper considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz…
In this paper, we consider the stabilization of wave equations with moving boundary. First, we show the solution behaviour of wave equation with Neumann boundary conditions, that is, the energy of wave equation with mixed boundary…
In this article, we study the coupling of the Einstein field equations of general relativity to a family of models of nonlinear electromagnetic fields. The family comprises all covariant electromagnetic models that satisfy the following…
We discuss high order absorbing constraint preserving boundary conditions for the Z4c formulation of general relativity coupled to the moving puncture family of gauges. We are primarily concerned with the constraint preservation and…
In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these…
We prove global stability of Minkowski space for the Einstein vacuum equations in harmonic (wave) coordinate gauge for the set of restricted data coinciding with Schwartzschild solution in the neighborhood of space-like infinity. The result…
This paper presents two kinds of strategies to construct structure-preserving algorithms with homogeneous Neumann boundary conditions for the sine-Gordon equation, while most existing structure-preserving algorithms are only valid for zero…
Numerical simulation of the spherically symmetric Einstein--Euler (EE) system faces severe challenges due to the stringent physical admissibility constraints of relativistic fluids and the geometric singularities inherent in metric…
We review recent efforts to re-formulate the Einstein equations for fully relativistic numerical simulations. In order to complete a long-term and accurate simulations of binary compact objects, people seek a robust set of equations against…