Related papers: Boundary Conditions for the Einstein Evolution Sys…
A persistent challenge in numerical relativity is the correct specification of boundary conditions. In this work we consider a many parameter family of symmetric hyperbolic initial-boundary value formulations for the linearized Einstein…
Evolution of a universe with homogeneous extra dimensions is studied with the benefit of a well-chosen parameter space that provides a systematic, useful, and convenient way for analysis. In this model we find a natural evolution pattern…
Boundary conditions may change the phase diagram of non-equilibrium statistical systems like the one-dimensional asymmetric simple exclusion process with and without particle number conservation. Using the quantum Hamiltonian approach, the…
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…
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…
The occurrence of a spacetime singularity indicates the breakdown of Einstein gravitation theory in these extreme regimes. We consider here the singularity issue and various black hole paradoxes at classical and quantum levels. It is…
We show how to use boundary conditions to drive the evolution on a Quantum Mechanical system. We will see how this problem can be expressed in terms of a time-dependent Schr\"{o}dinger equation. In particular we will need the theory of…
We provide a detailed analysis of several aspects of the turduckening technique for evolving black holes. At the analytical level we study the constraint propagation for a general family of BSSN-type formulation of Einstein's field…
A refined version of a recently introduced method for analysing the dynamics of an inhomogeneous irrotational dust universe is presented. A fully non-perturbative numerical computation of the time dependence of volume in this framework…
This is the second in a series of papers describing a 3+1 computational scheme for the numerical simulation of dynamic black hole spacetimes. We discuss the numerical time-evolution of a given black-hole-containing initial data slice in…
We use partial differential equations (PDEs) to describe physical systems. In general, these equations include evolution and constraint equations. One method used to find solutions to these equations is the Free-evolution approach, which…
We consider a particular example of dynamical compactification of an anisotropic 7+1 dimensional Universe in Einstein - Gauss - Bonnet gravity. Starting from rather general totally anisotropic initial conditions a Universe in question…
While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two…
In this article we further develop the solution theory for the Einstein constraint equations on an n-dimensional, asymptotically Euclidean manifold M with interior boundary S. Building on recent results for both the asymptotically Euclidean…
A systematic way of generating sets of local boundary conditions on the gauge fields in a path integral is presented. These boundary conditions are suitable for one--loop effective action calculations on manifolds with boundary and for…
The stability of Einstein static universe against homogeneous scalar perturbations in the context of braneworld scenario is investigated. The stability regions are obtained in terms of the constant geometric linear equation of state…
The aim of this article is to construct initial data for the Einstein equations on manifolds of the form R n+1 x T m , which are asymptotically flat at infinity, without assuming any symmetry condition in the compact direction. We use the…
In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…
A set of boundary conditions defining a non-rotating isolated horizon are given in Einstein-Maxwell theory. A space-time representing a black hole which itself is in equilibrium but whose exterior contains radiation admits such a horizon .…
We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x>0, t>0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and…