Related papers: A hyperbolic tetrad formulation of the Einstein eq…
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…
We derive a new symmetric hyperbolic formulation of the Einstein-Euler equations in Lagrange coordinates that are adapted to the Frauendiener-Walton formulation of the Euler equations. As an application, we use this system to show that the…
This is the second in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper the numerical methods used to solve the system of evolution…
We present a physically plausible solution representing Einstein's cluster mimicking the behaviors of compact star in the context of teleparallel equivalent of general relativity. The Teleparallel gravity (TEGR) is an alternative…
We study asymptotically constrained systems for numerical integration of the Einstein equations, which are intended to be robust against perturbative errors for the free evolution of the initial data. First, we examine the previously…
General relativity under the assumption of noncommuting components of the tetrad field is considered in this paper. Since the algebraic properties of the tetrad field representing the gravitational field are assumed to correspond to the…
With the aim of deriving symmetric hyperbolic free-evolution systems for GR that possess Hamiltonian structure and allow for the popular puncture gauge condition we analyze the hyperbolicity of Hamiltonian systems. We develop helpful tools…
Spacetimes, which are representations of a bridge-like geometry in gravity theory, are constructed as vacuum solutions to the first order equations of motion. Each such configuration consists of two copies of an asymptotically flat sheet,…
We establish a variant, which has the advantage of introducing only physical characteristics, of the symmetric quasi linear first order system given by H.\ Friedrich for the evolution equations of gravitating fluid bodies in General…
We exploit an interpretation of gravity as the symmetry broken phase of a de Sitter gauge theory to construct new solutions to the first order field equations. The new solutions are constructed by performing large $Spin(4,1)$ gauge…
We prove a global well-posedness and asymptotic convergence theorem for the \((3+1)\)-dimensional vacuum Einstein equations with positive cosmological constant \(\Lambda\) on globally hyperbolic spacetimes \(\widetilde M \cong M \times…
General relativity dynamics can be derived from different actions -- which depart from the Einstein-Hilbert action in boundary terms -- and for different choices of the dynamical variables. Among them, the teleparallel equivalent of general…
Based on the Arnowitt-Deser-Misner (ADM) canonical formulation of general relativity, a canonical formulation of gravitationally interacting classical spinning-object systems is given to linear order in spin. The constructed position,…
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)…
The ADM Hamiltonian formulation of general relativity with prescribed lapse and shift is a weakly hyperbolic system of partial differential equations. In general weakly hyperbolic systems are not mathematically well posed. For well…
The models of New General Relativity have recently got attention of research community, and there are some works studying their dynamical properties. The formal aspects of this investigation have been mostly restricted to the primary…
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…
A discussion of asymptotic weak and strong Poincare' charges in metric gravity is given to identify the proper Hamiltonian boundary conditions. The asymptotic part of the lapse and shift functions is put equal to their analogues on…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
Teleparallel gravity is a modified theory of gravity for which the Ricci scalar $R$ of the underlying geometry in the action is replaced by an arbitrary functional form of torsion scalar $T$. In doing so, cosmology in $% f(T)$ gravity…