Related papers: On the Initial Data Constraints on the Light cone …

The weak-field limit of Einstein--Cartan (EC) relativity is studied. The equations of EC theory are rewritten such that they formally resemble those of Einstein General Relativity (EGR); this allows ideas from post-Newtonian theory to be…

Discretized light-cone quantization of (3+1)-dimensional electrodynamics is discussed, with careful attention paid to the interplay between gauge choice and boundary conditions. In the zero longitudinal momentum sector of the theory a…

The geodesic-light-cone (GLC) coordinates are a useful tool to analyse light propagation and observations in cosmological models. In this article, we propose a detailed, pedagogical, and rigorous introduction to this coordinate system,…

The Einstein evolution equations are studied in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasilinear elliptic--hyperbolic system of evolution…

We define the stretched future light cone, a timelike hypersurface composed of the worldlines of radially accelerating observers with constant and uniform proper acceleration. By attributing temperature and entropy to this hypersurface, we…

With the dark energy phenomena explored over a decade, in this present work we discuss a specific case of the generalized Einstein-aether theories, in which the modified Friedmann Equation is similar to that in the Dvali-Gabadadze-Porrati…

In the Bondi-Sachs gauge, the Einstein equations with a cosmological constant coupled to a scalar field in spherical symmetry are cast into a first order strongly hyperbolic formulation in which the lapse and shift are the fundamental…

Gauge-invariant treatments of the second-order cosmological perturbation in a four dimensional homogeneous isotropic universe are formulated without any gauge fixing. We have derived the Einstein equations in the case of the single perfect…

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…

We consider a parabolic obstacle problem for Euler's elastic energy of graphs with fixed ends. We show global existence, well-posedness and subconvergence provided that the obstacle and the initial datum are suitably 'small'. For symmetric…

A simple derivation of the static Gross-Pitaevskii (GP) equation is given from an energy variational principle. The result is then generalized heuristically to the time-dependent GP form. With this as background, a number of different…

There exist several ways of constructing general relativity from `first principles': Einstein's original derivation, Lovelock's results concerning the exceptional nature of the Einstein tensor from a mathematical perspective, and…

We prove that analytic initial data on a light cone arising from a metric satisfying a "near-roundness" condition near the vertex lead to a solution of the vacuum Einstein equations to the future of the light-cone.

We reformulate the transport equation which determines the size, shape and orientation of infinitesimal light beams in arbitrary spacetimes. The behaviour of such light beams near vertices and conjugate points is investigated, with special…

We discuss the implementation, to the case of compact manifolds, of the perturbative method of Friedrich-Butscher for the construction of solutions to the vaccum Einstein constraint equations. This method is of a perturbative nature and…

This article is concerned with the study of weak solutions of a linear transport equation on a bounded domain with coupled boundary data for general non smooth space and time dependent velocity fields. The existence of solutions, its…

We prove the global stability of the Minkowski space viewed as the trivial solution of the Einstein-Vlasov system. To estimate the Vlasov field, we use the vector field and modified vector field techniques developed in [FJS15; FJS17]. In…

We review the properties of the constraint equations, from their geometric origin in hypersurface geometry through to their roles in the Cauchy problem and the Hamiltonian formulation of the Einstein equations. We then review properties of…

There is a constrained-WZNW--Toda theory for any simple Lie algebra equipped with an integral gradation. It is explained how the different approaches to these dynamical systems are related by gauge transformations. Combining Gauss…

Given a truncated incoming null cone and a truncated outgoing null cone intersecting at a two sphere $S$ with smooth characteristic initial data, a theorem of Rendall shows that the vacuum Einstein equations can be solved in a small…