Related papers: Evolution systems for non-linear perturbations of …
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…
We investigate the evolution of cosmological perturbations in models of dark energy described by a time-like unit normalized vector field specified by a general function $\mathcal{F}(\mathcal{K})$, so-called Generalized Einstein-Aether…
The hyperboloidal initial value problem is addressed in the context of Numerical Relativity, motivated by its use of hyperboloidal slices - smooth spacelike slices that reach future null infinity, the "place" in spacetime where radiation is…
We present an analysis of well-posedness of constrained evolution of 3+1 formulations of GR. In this analysis we explicitly take into account the energy and momentum constraints as well as possible algebraic constraints on the evolution of…
This is the first of a series of papers describing a numerical implementation of the conformally rescaled Einstein equation, an implementation designed to calculate asymptotically flat spacetimes, especially spacetimes containing black…
Density perturbations and their dynamic evolution from early to late times can be used for an improved understanding of interesting physical phenomena both in cosmology and in the context of heavy-ion collisions. We discuss the spectrum and…
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…
Vacuum solutions to the Einstein equations can be viewed as the interplay between the geometry and the gravitational wave energy content. The constraints on initial data reflect this interaction. We assume we are looking at cosmological…
We uncover a symmetry of the linear Einstein equations near extremal horizons. Specifically, acting with a spherically symmetric linearized diffeomorphism on the perturbative solutions to the Einstein-Maxwell equations in the…
General relativity can describe various gravitational systems of astrophysical relevance, like black holes and neutron stars, or even strongly coupled systems through the holographic duality. The characteristic initial (boundary) value…
We derive a new first-order formulation for Einstein's equations which involves fewer unknowns than other first-order formulations that have been proposed. The new formulation is based on the 3+1 decomposition with arbitrary lapse and…
We linearize vacuum Einstein field equations with a cosmological constant around a curved background to elaborate on the reconstruction of the Abbott-Deser charges and incorporate a spin connection into the definition using the algebra of…
We present a numerical study of the Einstein equations, according to the Arnowitt-Deser-Misner (ADM) formalism, in order to simulate the dynamics of gravitational fields. We took in consideration the original $3+1$ decomposition of the ADM…
We consider a complex scalar field minimally coupled to gravity and to a U(1) gauge symmetry and we construct of a first order symmetric hyperbolic evolution system for the Einstein-Maxwell-Klein-Gordon system. Our analysis is based on a…
A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon system with spherical symmetry is presented. Initial data are specified on the union of a space-like and null hypersurface. The development of the data is obtained…
The linear Einstein-Boltzmann equations describe the evolution of perturbations in the universe and its numerical solutions play a central role in cosmology. We revisit this system of differential equations and present a detailed…
A refined version of a recently introduced method for analysing the dynamics of an inhomogeneous irrotational dust universe is presented. A fully non-perturbative numerical computation of the time dependence of volume in this framework…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
We propose a new approach for the solution of initial value problems for integrable evolution equations in the periodic setting based on the unified transform. Using the nonlinear Schr\"odinger equation as a model example, we show that the…
We study the initial value problem for the Einstein-Klein-Gordon system and establish the global nonlinear stability of massive matter in the near-Minkowski regime when the initial geometry is a perturbation of an asymptotically flat,…