Related papers: Evolution equations for the perturbations of slowl…
We present a new derivation of the perturbation equations governing the oscillations of relativistic non-rotating neutron star models using the ADM-formalism. This formulation has the advantage that it immediately yields the evolution…
We present a hyperbolic formulation of the evolution equations describing non-radial perturbations of slowly rotating relativistic stars in the Regge--Wheeler gauge. We demonstrate the stability preperties of the new evolution set of…
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 Einstein evolution equations have been written in a number of symmetric hyperbolic forms when the gauge fields--the densitized lapse and the shift--are taken to be fixed functions of the coordinates. Extended systems of evolution…
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…
It was shown recently that the constraints on the initial data for Einstein's equations may be posed as an evolutionary problem [9]. In one of the proposed two methods the constraints can be replaced by a first order symmetrizable…
The formulation of the initial value problem for the Einstein equations is at the heart of obtaining interesting new solutions using numerical relativity and still very much under theoretical and applied scrutiny. We develop a specialised…
The causal structure of Einstein's evolution equations is considered. We show that in general they can be written as a first order system of balance laws for any choice of slicing or shift. We also show how certain terms in the evolution…
Recently a Hamiltonian formulation for the evolution of the universe dominated by multiple oscillatory scalar fields was developed by the present author and was applied to the investigation of the evolution of cosmological perturbations on…
We review recent efforts to re-formulate the Einstein equations for fully relativistic numerical simulations. The so-called numerical relativity (computational simulations in general relativity) is a promising research field matching with…
A gauge-invariant, linear cosmological perturbation theory of an almost homogeneous and isotropic universe with dynamically evolving Newton constant G and cosmological constant $\Lambda$ is presented. The equations governing the evolution…
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic…
We consider the perturbations of a relativistic star as an initial-value problem. Having discussed the formulation of the problem (the perturbation equations and the appropriate boundary conditions at the centre and the surface of the star)…
We describe a set of time evolution equations and its numerical implementation for the investigation of non-axisymmetric oscillations of rapidly rotating compact objects in full General Relativity, taking into account the contribution of a…
Non-axisymmetric oscillations of rapidly rotating relativistic stars are studied using the Cowling approximation. The oscillation spectra have been estimated by Fourier transforming the evolution equations describing the perturbations. This…
Einstein's system of equations in the ADM decomposition involves two subsystems of equations: evolution equations and constraint equations. For numerical relativity, one typically solves the constraint equations only on the initial time…
We study the evolution of linear perturbations in a Lema\^itre-Tolman-Bondi (LTB) void model with realistic cosmological initial conditions. Linear perturbation theory in LTB models is substantially more complicated than in standard…
This is the second in a series of papers on the construction and validation of a three-dimensional code for the solution of the coupled system of the Einstein equations and of the general relativistic hydrodynamic equations, and on the…
We present a new formulation to construct numerically equilibrium configurations of rotating stars in general relativity. Having in mind the application to their quasi static evolutions, we adopt a Lagrangian formulation of our own…
We review recent efforts to re-formulate the Einstein equations for fully relativistic numerical simulations. In order to complete a long-term and accurate simulations of binary compact objects, people seek a robust set of equations against…