Related papers: Regularity for Harmonic - Einstein Equation
We introduce consideration of a new factor, synchronisation of spacetime Mixmaster oscillations, that may play a simplifying role in understanding the nature of the general inhomogeneous cosmological solution to Einstein's equations. We…
The Einstein-Bianchi system uses symmetric and traceless tensors to reformulate Einstein's original field equations. However, preserving these algebraic constraints simultaneously remains a challenge for numerical methods. This paper…
We prove definitive results on the global stability of the flat space among solutions of the Einstein-Klein-Gordon system. Our main theorems in this monograph include: (1) A proof of global regularity (in wave coordinates) of solutions of…
We consider discretizations of the Einstein action of general relativity such that the resulting discrete equations of motion form a consistent constrained system. Upon ``spin foam'' quantization of the system, consistency allows a natural…
We investigate a simple variation of the Generalized Harmonic method for evolving the Einstein equations. A flat space wave equation for metric perturbations is separated from the Ricci tensor, with the rest of the Ricci tensor becoming a…
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…
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention…
The strong unique continuation property for Einstein metrics can be concluded from the well-known fact that Einstein metrics are analytic in geodesic normal coordinates. Here we give a proof of the same result that given two Einstein…
We develop the regularity theory of the spatially homogeneous Boltzmann equation with cut-off and hard potentials (for instance, hard spheres), by (i) revisiting the Lp-theory to obtain constructive bounds, (ii) establishing propagation of…
In this article we study the stability problem for the Einstein-Hilbert functional on compact symmetric spaces following and completing the seminal work of Koiso on the subject. We classify in detail the irreducible representations of…
We prove the linear stability with respect to the Einstein-Hilbert action of the symmetric spaces $\mathrm{SU}(n)$, $n\geq3$, and $E_6/F_4$. Combined with earlier results, this resolves the stability problem for irreducible symmetric spaces…
The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's…
In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.
In a Hilbert space setting, we study the stability properties of the regularized continuous Newton method with two potentials, which aims at solving inclusions governed by structured monotone operators. The Levenberg-Marquardt…
The paper proves existence of renormalized stationary solutions for a dense class of discrete velocity Boltzmann equations in the plane with given ingoing boundary values. The proof is based on the construction of a sequence of…
We derive a unique continuation theorem for the vacuum Einstein equations. Our method of proof utilizes Carleman estimates (most importantly one obtained recently by Ionescu and Klainerman), but also relies strongly on certain geometric…
Einstein equations are addressed with the energy-momentum tensor that appears if the equations under discussion are required to possess conformal invariance. It is proved that thus derived equations (equations of conformally invariant…
In this paper, we study the regularity for viscosity solutions of locally uniformly elliptic equations and obtain a series of interior pointwise $C^{k,\alpha}$ ($k\geq 1$, $0<\alpha<1$) regularity with smallness assumptions on the solution…
We show that C^2 conformally compact Riemannian Einstein metrics have conformal compactifications that are smooth up to the boundary in dimension 3 and all even dimensions, and polyhomogeneous in odd dimensions greater than 3.
We construct low regularity solutions of the vacuum Einstein constraint equations on compact manifolds. On 3-manifolds we obtain solutions with metrics in $H^s$ where $s>3/2$. The constant mean curvature (CMC) conformal method leads to a…