Related papers: On the evolution equations for a self-gravitating …
We examine the problem of the construction of a first order symmetric hyperbolic evolution system for the Einstein-Maxwell-Euler system. Our analysis is based on a 1+3 tetrad formalism which makes use of the components of the Weyl tensor as…
In order to study the gravitational collapse of charged matter we analyze the simple model of an self-gravitating massless scalar field coupled to the electromagnetic field in spherical symmetry. The evolution equations for the…
A frame representation is used to derive a first order quasi-linear symmetric hyperbolic system for a scalar field minimally coupled to gravity. This procedure is inspired by similar evolution equations introduced by Friedrich to study the…
We develop and apply a fully covariant 1+3 electromagnetic analogy for gravity. The free gravitational field is covariantly characterized by the Weyl gravito-electric and gravito-magnetic spatial tensor fields, whose dynamical equations are…
We review some well posed formulations of the evolution part of the Cauchy problem of General Relativity that we have recently obtained. We include also a new first order symmetric hyperbolic system based directly on the Riemann tensor and…
We incorporate a massless scalar field into a 3-dimensional code for the characteristic evolution of the gravitational field. The extended 3-dimensional code for the Einstein--Klein--Gordon system is calibrated to be second order…
Motivated by the goal for high accuracy modeling of gravitational radiation emitted by isolated systems, recently, there has been renewed interest in the numerical solution of the hyperboloidal initial value problem for Einstein's field…
We consider the Einstein-Maxwell-Klein-Gordon equations for a spherically symmetric scalar field scattering off a Reissner-Nordstr\"om black hole in asymptotically flat spacetime. The equations are solved numerically using a hyperboloidal…
Using the first-order approximating solutions to the Einstein-Maxwell-Klein-Gordon system of equations for a complex scalar field minimally coupled to a spherically symmetric spacetime, we study the feedback of gravity and electric field on…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
The main purpose of this contribution is to determine physical and geometrical characterizations of whole classes of stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the $(2+1)$-dimensional…
This paper invokes a new mechanism for reducing a coupled system of fields (including Einstein's equations without a cosmological constant) to equations that possess solutions exhibiting characteristics of immediate relevance to current…
We consider the global evolution problem for Einstein's field equations in the near-Minkowski regime and study the long-time dynamics of a massive scalar field evolving under its own gravitational field. We establish the existence of a…
Utilizing the autonomous system of ordinary differential equations derived in arXiv:1809.01458 to define the evolution, we further investigate a class of cosmological models within an Einstein-aether gravitational framework by introducing a…
Significant advances were made in recent years on the global evolution problem for self-gravitating massive matter in the small-perturbative regime close to Minkowski spacetime. To study the coupling between a Klein-Gordon equation and…
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…
Starting from the chiral first-order pure connection formulation of General Relativity, we put the field equations of GR in a strikingly simple evolution system form. The two dynamical fields are a complex symmetric tracefree 3x3 matrix…
A scale invariant, Weyl geometric, Lagrangian approach to cosmology is explored, with a a scalar field phi of (scale) weight -1 as a crucial ingredient besides classical matter \cite{Tann:Diss,Drechsler:Higgs}. For a particularly simple…
We propose an Einstein-{\ae}ther scalar-tensor cosmological model. In particular in the scalar-tensor Action Integral we introduce the {\ae}ther field with {\ae}ther coefficients to be functions of the scalar field. This cosmological model…
We determine exact and analytic solutions of the gravitational field equations in Einstein-aether scalar model field with a Bianchi I background space. In particular, we consider nonlinear interactions of the scalar field with the aether…