Related papers: A hyperbolic tetrad formulation of the Einstein eq…
We show how the basic idea of parabolic Jacobi relaxation can be modified to obtain a new class of hyperbolic relaxation schemes that are suitable for the solution of elliptic equations. Some of the analytic and numerical properties of…
We identify a symplectic potential for general relativity in tetrad and connection variables that is fully gauge-invariant, using the freedom to add surface terms. When torsion vanishes, it does not lead to surface charges associated with…
The teleparallel equivalent of general relativity (TEGR) is represented in a field-theoretical form, where tetrad and matter perturbations are propagated on a background solution of TEGR. Thus, the background tetrad and metric satisfy the…
We show that the Kerr-Schild ansatz can be extended from the metric to the tetrad, and then to teleparallel gravity where curvature vanishes but torsion does not. We derive the equations of motion for the Kerr-Schild null vector, and…
Teleparallel geometry utilizes Weitzenb\"ock connection which has nontrivial torsion but no curvature and does not directly follow from the metric like Levi-Civita connection. In extended teleparallel theories, for instance in $f(T)$ or…
TeVeS uses a dynamical vector field with timelike unit norm constraint to specify a preferred local frame. When matter moves slowly in this frame - the so-called quasi-static regime - Modified Newtonian Dynamics (MoND) results. Theories…
It is traditionally believed that the Lorentz transformations (LT) and Einstein's theorem of velocity addition (ETVA), underlying special relativity, cannot be obtained from non-relativistic (classical) mechanics. In the present paper it is…
In this work we study Berwald spacetimes and their vacuum dynamics, where the latter are based on a Finsler generalization of the Einstein's equations derived from an action on the unit tangent bundle. In particular, we consider a specific…
We introduce the generalized Lorentz gauge condition in the theory of quantum electrodynamics into the general vector-tensor theories of gravity. Then we explore the cosmic evolution and the static, spherically symmetric solution of the…
In order to perform accurate and stable long-term numerical integration of the Einstein equations, several hyperbolic systems have been proposed. We here report our numerical comparisons between weakly hyperbolic, strongly hyperbolic, and…
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…
Local Lorentz transformations play an important role in teleparallel gravity theories, in which a tetrad is conventionally employed as a fundamental field variable describing the gravitational field. It is commonly understood that…
We study the energy and momentum of an isolated system in the tetrad theory of gravitation, starting from the most general Lagrangian quadratic in torsion, which involves four unknown parameters. When applied to the static spherically…
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…
We discuss the initial-boundary value problem of General Relativity. Previous considerations for a toy model problem in electrodynamics motivate the introduction of a variational principle for the lapse with several attractive properties.…
We generate new spherical and time-dependent solutions of viable Horndeski gravity by disforming a solution of the Einstein equations with scalar field source and positive cosmological constant. They describe dynamical objects embedded in…
In the 3+1 framework of the Einstein equations for the case of vanishing shift vector and arbitrary lapse, we calculate explicitly the four boundary equations arising from the vanishing of the projection of the Einstein tensor along the…
The Regge-Teitelboim formulation of gravity, which utilizes dynamical embeddings in a background space, effectively introduces source terms in the standard Einstein equations that are not attributable to the energy-momentum tensor. We show…
We analyse the mathematical underpinnings of a mixed hyperbolic-elliptic form of the Einstein equations of motion in which the lapse function is determined by specified mean curvature and the shift is arbitrary. We also examine a new…
We present an overview of recent developments in the numerical solution of Horndeski gravity theories, which are the class of all scalar-tensor theories of gravity that have second order equations of motion. We review several methods that…