Related papers: Outer boundary conditions for Einstein's field equ…
A detailed account is given on approximation schemes to the Einstein theory of general relativity where the iteration starts from the Newton theory of gravity. Two different coordinate conditions are used to represent the Einstein field…
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…
This work is a continuation of [E. Bonnetier, D.Bresch, V. Milisic, submitted]; it deals with rough boundaries in the simplified context of a Poisson equation. We impose Dirichlet boundary conditions on the periodic microscopic perturbation…
In this work two different boundary conditions for first order gravity, corresponding to a null and a negative cosmological constant respectively, are studied. Both boundary conditions allows to obtain the standard black hole…
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…
In principle, global properties of solution of Einstein equations need to be addressed using the conformal Einstein equations, because this conformal compactification allows a clean definition of the `infinities' (spacelike, timelike and…
We introduce a new class of absorbing boundary conditions (ABCs) for the Helmholtz equation. The proposed ABCs are obtained by using $L$ discrete layers and the $Q_N$ Lagrange finite element in conjunction with the $N$-point Gauss-Legendre…
We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the…
Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be…
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…
The dynamics of quantum field theories on bounded domains requires the introduction of boundary conditions on the quantum fields. We address the problem from a very general perspective by using charge conservation as a fundamental principle…
Absorbing boundary conditions are presented for three-dimensional time-dependent Schr\"odinger-type of equations as a means to reduce the cost of the quantum-mechanical calculations. The boundary condition is first derived from a…
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 revisit the propagation of classical scalar fields in a spacetime which is asymptotically anti-de Sitter. The lack of global hyperbolicity of the underlying background gives rise to an ambiguity in the dynamical evolution of solutions of…
We prove the existence of asymptotically hyperbolic solutions to the vacuum Einstein constraint equations with a marginally outer trapped boundary of positive mean curvature, using the constant mean curvature conformal method. As an…
The regular finite initial value problem at infinity is used to obtain regularity conditions on the freely specifiable parts of initial data for the vacuum Einstein equations with non-vanishing second fundamental form. These conditions…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
We study Dirac quasinormal modes of Schwarzschild-Anti-de Sitter (Schwarzschild-AdS) black holes, following the generic principle for allowed boundary conditions proposed in \cite{PhysRevD.92.124006}. After deriving the equations of motion…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
The paper is devoted to constructing the global solutions around global Maxwellians to the initial-boundary value problem on the Boltzmann equation in general bounded domains with isothermal diffuse reflection boundaries. We allow a class…