Related papers: Solving the Einstein Equations Numerically
This paper constitutes a background to the paper 'Quantum mechanics as "space-time statistical mechanics"?', arXiv:quant-ph/0501133, presented previously by the author. But it is also a free-standing and self-contained paper. The purpose of…
The Earth's geoid is one of the most essential and fundamental concepts to provide a gravity field-related height reference in geodesy and associated sciences. To keep up with the ever-increasing experimental capabilities and to…
A general covariant extension of Einstein's field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector. The extended field equations,…
An outstanding issue in the treatment of boundaries in general relativity is the lack of a local geometric interpretation of the necessary boundary data. For the Cauchy problem, the initial data is supplied by the 3-metric and extrinsic…
A fundamental problem of Einstein's theory of classical general relativity is the existence of singularities such as the big bang. All known laws of physics end at these boundaries of classical space-time. Thanks to recent developments in…
In the standard cosmological theory one uses the Einstein concepts of space and time as were originally introduced for the special theory of relativity and the general relativity theory. According to this approach all physical quantities…
Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is…
We find initial data for numerical relativity simulations of inhomogeneous cosmologies. This involves treating an exceptional case of the general relativity constraint equations. We devise analytic and numerical methods to treat this…
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…
The numerous ways of introducing spatial gravitational forces are fit together in a single framework enabling their interrelationships to be clarified. This framework is then used to treat the ``acceleration equals force" equation and…
Well-posedness of the initial (boundary) value problem is an essential property, both of meaningful physical models and of numerical applications. To prove well-posedness of wave-type equations their level of hyperbolicity is an essential…
We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.
We propose a formulation of gravity theory in the form of a field theory in a flat space-time with a number of dimensions greater than four. Configurations of the field under consideration describe the splitting of this space-time into a…
Every spacetime is defined by its metric, the mathematical object which further defines the spacetime curvature. From the relativity principle, we have the freedom to choose which coordinate system to write our metric in. Some coordinate…
We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in a wide class of modified theories of gravity. The code utilizes a relaxed Newton-Raphson method to…
Numerical simulations are becoming a more effective tool for conducting detailed investigations into the evolution of our universe. In this article, we show how the framework of numerical relativity can be used for studying cosmological…
An alternative approach to Einstein's theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian…
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local in time Cauchy problem, which is relatively well understood, is…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
In Einstein's general relativity, with its nonlinear field equations, the discoveries and analyzes of various specific explicit solutions made a great impact on understanding many of the unforeseen features of the theory. Some solutions…