Related papers: Toward standard testbeds for numerical relativity
All of the experiments supporting Einstein's Special Relativity Theory are also supportive of the Lorentz ether theory, or many other ether theories. However, a growing number of experiments show deviations from Einstein's Special…
Exact solutions to the Einstein field equations may be generated from already existing ones (seed solutions), that admit at least one Killing vector. In this framework, a space of potentials is introduced. By the use of symmetries in this…
This work deals with the one-dimensional Stefan problem with a general time-dependent boundary condition at the fixed boundary. Stochastic solutions are obtained using discrete random walks, and the results are compared with analytic…
Incremental learning from non-stationary data poses special challenges to the field of machine learning. Although new algorithms have been developed for this, assessment of results and comparison of behaviors are still open problems, mainly…
This paper is concerned exclusively with axisymmetric spacetimes. We want to develop reductions of Einstein's equations which are suitable for numerical evolutions. We first make a Kaluza-Klein type dimensional reduction followed by an ADM…
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…
This thesis is concerned with formulations of the Einstein equations in axisymmetric spacetimes which are suitable for numerical evolutions. We develop two evolution systems based on the (2+1)+1 formalism. The first is a (partially)…
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…
Quantum hypothesis testing concerns the discrimination between quantum states. This paper introduces a novel lower bound for asymmetric quantum hypothesis testing that is based on the Nussbaum-Szko{\l}a mapping. The lower bound provides a…
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…
We study the effect of small-scale inhomogeneities for Einstein clusters. We construct a spherically symmetric stationary spacetime with small-scale radial inhomogeneities and propose the Gedankenexperiment. An hypothetical observer at the…
Relativistic simulations in 3+1 dimensions typically monitor the Hamiltonian and momentum constraints during evolution, with significant violations of these constraints indicating the presence of instabilities. In this paper we rewrite the…
The characteristic approach to numerical relativity is a useful tool in evolving gravitational systems. In the past this has been implemented using two patches of stereographic angular coordinates. In other applications, a six-patch angular…
Outer boundary conditions for strongly and symmetric hyperbolic formulations of 3D Einstein's field equations with a live gauge condition are discussed. The boundary conditions have the property that they ensure constraint propagation and…
We present SphericalNR, a new framework for the publicly available Einstein Toolkit that numerically solves the Einstein field equations coupled to the equations of general relativistic magnetohydrodynamics (GRMHD) in a 3+1 split of…
A strongly well-posed initial boundary value problem based upon constraint-preserving boundary conditions of the Sommerfeld type has been established for the harmonic formulation of the vacuum Einstein's equations. These Sommerfeld…
We perform large-scale cosmological simulations that solve Einstein's equations directly via numerical relativity. Starting with initial conditions sampled from the cosmic microwave background, we track the emergence of a cosmic web without…
A first order symmetric hyperbolic tetrad formulation of the Einstein equations developed by Estabrook and Wahlquist and put into a form suitable for numerical relativity by Buchman and Bardeen (the WEBB formulation) is adapted to explicit…
We present a new method of extracting gravitational radiation from three-dimensional numerical relativity codes and providing outer boundary conditions. Our approach matches the solution of a Cauchy evolution of Einstein's equations to a…
A new gauge driver is introduced for the generalized harmonic (GH) representation of Einstein's equation. This new driver allows a rather general class of gauge conditions to be implemented in a way that maintains the hyperbolicity of the…