Related papers: Linearized gravitational waves near space-like and…

A non-canonical correspondence of the complete sets of solutions to the Dirac and Klein-Gordon free equations in Minkowski space-time is established. This allows for a novel viewpoint on the relationship of relativistic equations for…

The hypothesis of an alternative way of obtaining gravitational waves is the physical motivation of this article. Using the linear field approximation and a symmetry transformation of the affine connection, new field equations and new gauge…

Exact solutions for nonexpanding impulsive waves in a background with nonzero cosmological constant are constructed using a `cut and paste' method. These solutions are presented using a unified approach which covers the cases of de Sitter,…

Spin-2, spin-1 and spin-0 modes in linearised teleparallelism are obtained where the totally skew-symmetric complex contortion tensor generates scalar torsion waves and the symmetric contortion in the last two indices generates…

We explicitly express the Minkowski vacuum of a massless scalar field in terms of the particle notion associated with suitable spherical conformal killing fields. These fields are orthogonal to the light wavefronts originating from a sphere…

In this paper, we study the linear wave equations in an asymptotically anti-de Sitter spacetime. We will consider the mixed boundary problem, where the initial data are given on an outgoing null hypersurface and a timelike hypersurface, and…

Zero rest-mass fields of spin 1 (the electromagnetic field) and spin 2 propagating on flat space and their corresponding Newman-Penrose (NP) constants are studied near spatial infinity. The aim of this analysis is to clarify the…

In this paper we show the small data solvability of suitable semilinear wave and Klein-Gordon equations on geometric classes of spaces, which include so-called asymptotically de Sitter and Kerr-de Sitter spaces, as well as asymptotically…

We use the conformal approach to numerical relativity to evolve hyperboloidal gravitational wave data without any symmetry assumptions. Although our grid is finite in space and time, we cover the whole future of the initial data in our…

Minkowski space is shown to be globally stable as a solution to the Einstein--Vlasov system in the case when all particles have zero mass. The proof proceeds by showing that the matter must be supported in the "wave zone", and then proving…

We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to…

A new method for computing exact conformal partial wave expansions is developed and applied to approach the problem of Hilbert space (Wightman) positivity in a non-perturbative four-dimensional quantum field theory model. The model is based…

The null splitting theorem (proved in math.DG/9909158) is discussed. As an application, a uniqueness theorem for Minkowski space and for de Sitter space associated with the occurrence of null lines (inextendible globally achronal null…

These notes provide a student-friendly introduction to the theory of gravitational waves in full, non-linear general relativity (GR). We aim for a balance between physical intuition and mathematical rigor and cover topics such as the…

In the paper complete systems of exact solutions for Dirac and Weyl equations in the Lobachevsky space are constructed on the base of the method of separation of the variables in quasi-cartesian coordinates. An extended helicity operator is…

This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…

In the first part of the thesis, and after an introduction to certain models of modified gravity, we study consistent Lagrangians for Lorentz invariant (massive and massless) spin-2 and spin-3/2 particles in flat space. The second part of…

This paper addresses the fate of extended space-time symmetries, in particular conformal symmetry and supersymmetry, in two-dimensional Rindler space-time appropriate to a uniformly accelerated non-inertial frame in flat 1+1-dimensional…

Friedrich's proofs for the global existence results of de Sitter-like space-times and of semi-global existence of Minkowski-like space-times [Comm. Math. Phys. \textbf{107}, 587 (1986)] are re-examined and discussed, making use of the…

A physical interpretation is presented of the general class of conformally flat pure radiation metrics that has recently been identified by Edgar and Ludwig. It is shown that, at least in the weak field limit, successive wave surfaces can…