Related papers: A class of gauges for the Einstein equations
$[n+1]$-dimensional ($n\geq 3$) smooth Einsteinian spaces of Euclidean and Lorentzian signature are considered. The base manifold $M$ is supposed to be smoothly foliated by a two-parameter family of codimension-two-surfaces which are…
A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…
We propose a re-formulation of the Einstein evolution equations that cleanly separates the conformal degrees of freedom and the non-conformal degrees of freedom with the latter satisfying a first order strongly hyperbolic system. The…
Entanglement entropy (EE) in interacting field theories has two important issues: renormalization of UV divergences and non-Gaussianity of the vacuum. In this letter, we investigate them in the framework of the two-particle irreducible…
Einstein's static model is the first relativistic cosmological model. The model is static, finite and of spherical spatial symmetry. I use the solution of Einstein's field equations in a homogeneous and isotropic universe -- Friedmann's…
In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…
A solution of the Einstein vacuum field equations is constructed within the contex of perturbation theory. The solution possesses a graphical representation in terms of diagrams.
A new class of higher-dimensional exact solutions of Einstein's vacuum equation is presented. These metrics are written in terms of the exponential of a symmetric matrix and when this matrix is diagonal the solution reduces to…
If Einstein's equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric's null cone. The kinematical problem is solved using…
We present a general approach to the analysis of gauge stability of 3+1 formulations of General Relativity (GR). Evolution of coordinate perturbations and the corresponding perturbations of lapse and shift can be described by a system of…
For (2+2)-dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as…
The constraint equations for smooth $[n+1]$-dimensional (with $n\geq 3$) Riemannian or Lorentzian spaces satisfying the Einstein field equations are considered. It is shown, regardless of the signature of the primary space, that the…
We investigate the global dynamics of the field equations of (pure) quadratic theories of gravity which generalise Einstein's theory in spatially flat homogeneous and isotropic cosmological models with a perfect fluid. We introduce global…
Hyperbolic formulations of the equations of motion are essential technique for proving the well-posedness of the Cauchy problem of a system, and are also helpful for implementing stable long time evolution in numerical applications. We,…
Considering the spin-coefficient version of the left-flat vacuum Einstein equations, all but one of the fifty equations can be explicitly integrated via the introduction of five spin-weight s=-2 complex potentials. The final equation is a…
On a spacetime $(M,g)$ endowed with a density function $h$, we consider the vacuum weighted Einstein field equations: \[h\rho-\operatorname{Hes}_h+\Delta h g=0.\] First, it is shown that the equation characterizes critical metrics for an…
We present a heuristic analysis of the dynamics of general solutions to the Einstein Field Equations which highlights the possibility that such systems could possess a degree of unpredictability stronger than that which characterises…
We present a simple method to obtain vacuum solutions of Einstein's equations in parabolic coordinates starting from ones with cylindrical symmetries. Furthermore, a generalization of the method to a more general situation is given together…
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…
Various aspects of the Cauchy problem for the Einstein equations are surveyed, with the emphasis on local solutions of the evolution equations. Particular attention is payed to giving a clear explanation of conceptual issues which arise in…