Related papers: An Improved Gauge Driver for the Generalized Harmo…
By rescaling the Gauss-Bonnet (GB) coupling constant $\alpha \rightarrow \alpha/(D-4)$ and considering the $D \rightarrow 4$ limit, the GB gravity gives rise to nontrivial modification of general relativity in four dimensions. In this work,…
A new approach to gravitational gauge-invariant perturbation theory begins from the fourth-order Einstein-Ricci system, a hyperbolic formulation of gravity for arbitrary lapse and shift whose centerpiece is a wave equation for curvature. In…
The dual-frame formalism leads to an approach to extend numerical relativity simulations in generalized harmonic gauge (GHG) all the way to null infinity. A major setback is that without care, even simple choices of initial data give rise…
We investigate the properties of a fairly large class of boundary conditions for the linearised Einstein equations in the Riemannian setting, ones which generalise the linearised counterpart of boundary conditions proposed by Anderson.…
The Cauchy problem of the vacuum Einstein's equations aims to find a semi-metric $g_{\alpha\beta}$ of a spacetime with vanishing Ricci curvature $R_{\alpha,\beta}$ and prescribed initial data. Under the harmonic gauge condition, the…
Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here we demonstrate numerically, that they can be used for a…
Inflationary spatially homogeneous cosmological models within an Einstein-Aether gravitational framework are investigated. The matter source is assumed to be a scalar field which is coupled to the aether field expansion and shear scalars…
We report on the successful numerical evolution of the compactified hyperboloidal initial value problem in general relativity using generalized harmonic gauge. We work in spherical symmetry, using a massless scalar field to drive dynamics.…
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…
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational…
This paper explores stability of the Einstein universe against linear homogeneous perturbations in the background of $f(\mathcal{G},T)$ gravity. We construct static as well as perturbed field equations and investigate stability regions for…
We derive formulas for variations of mass, angular momentum and canonical energy in Einstein (n-2)-gauge form field theory by means of the ADM formalism. Considering the initial data for the manifold with an interior boundary which has the…
Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint…
Specifying boundary conditions continues to be a challenge in numerical relativity in order to obtain a long time convergent numerical simulation of Einstein's equations in domains with artificial boundaries. In this paper, we address this…
We attempt to study three significant tests of general relativity in higher dimensions both in commutative and non-commutative spaces. In the context of non-commutative geometry, we will consider a solution of the Einstein equation in…
In this paper, we study the phase space of cosmological models in the context of Einstein-Gauss-Bonnet theory. More specifically, we consider a generalized dynamical system that encapsulates the main features of the theory and for the cases…
We show how the use of the normal projection of the Einstein tensor as a set of boundary conditions relates to the propagation of the constraints, for two representations of the Einstein equations with vanishing shift vector: the ADM…
We analyze Einstein's vacuum field equations in generalized harmonic coordinates on a compact spatial domain with boundaries. We specify a class of boundary conditions which is constraint-preserving and sufficiently general to include…
To numerically evolve the full Einstein equations (or modifications thereof), simulations of cosmological spacetimes must rely on a particular formulation of the field equations combined with a specific gauge/frame choice. Yet truly…
Gauge invariant treatments of the second order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the…