Related papers: Brill Waves with Slow Fall-Off Towards Spatial Inf…
We prove the existence of small solitary waves for one-dimensional lattices of particles that each repel every other particle with a force that decays as a power of distance. For force exponents $\alpha+1$ with $\frac43<\alpha<3$, we employ…
In this paper we present in detail the numerical solution of the conformally invariant wave equation on top of a fixed background space-time corresponding to two different cases: i) 1+1 Minkowski space-time in Cartesian coordinates and ii)…
We discuss conformally flat plane wave solutions of Einstein equations depending on the plane wave phase $\xi=\omega\tau-{\bf qx}$, where $\tau$ is the conformal time. We show that ideal fluid Einstein equations and scalar fields with…
A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at…
We study spherically symmetric solutions to the Einstein-Euler equations which model an idealized relativistic neutron star surrounded by vacuum. These are barotropic fluids with a free boundary, governed by an equation of state which sets…
In previous work, the numerical solution of the linearized gravitational field equations near space-like and null-infinity was discussed in the form of the spin-2 zero-rest-mass equation for the perturbations of the conformal Weyl…
We study in a Brill-Hartle type of approximation the back reaction of a superposition of linear gravitational waves on the mean gravitational field up to second order in the wave amplitudes. The background field is taken as an…
An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect fluid solutions of Einstein's equations. For physically relevant…
We review recent mathematical results concerning the high-frequency solutions to the Einstein vacuum equations and the limits of these solutions. In particular, we focus on two conjectures of Burnett, which attempt to give an exact…
New exact vacuum solutions with various singularities in the plane-symmetric spacetime are shown, and they are applied to the analysis of inhomogeneous cosmological models and colliding gravitational waves. One of the singularities can be…
A new class of solutions to the coupled, spherically symmetric Einstein-Maxwell equations for a compact material source is constructed. Some of these solutions can be made to satisfy a number of requirements for being physically relevant,…
We describe the general structure of the spherically symmetric solutions in the Weyl conformal gravity. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the…
We demonstrate how plane fronted waves with colliding wave fronts are the asymptotic limit of spherical electromagnetic and gravitational waves. In the case of the electromagnetic waves we utilize Bateman's representation of radiative…
The purpose of this work is to investigate spatially homogeneous and flat cosmological solutions of the Einstein equations coupled to a non-variational ``near-minimal'' scalar field. This coupling model represents a minimal departure from…
A particular yet large class of non-diverging solutions which admits a cosmological constant, electromagnetic field, pure radiation and/or general non-null matter component is explicitly presented. These spacetimes represent exact…
Smooth Cauchy data for the Einstein-Lambda-vacuum field equations with positive cosmological constant Lambda that are sufficiently close to de Sitter data develop into a solution that admits a smooth conformal boundary Scri+ in its future.…
We express the Einstein-Vlasov system in spherical symmetry in terms of a dimensionless momentum variable $z$ (radial over angular momentum). This regularises the limit of massless particles, and in that limit allows us to obtain a reduced…
We present a new pseudospectral code, bamps, for numerical relativity written with the evolution of collapsing gravitational waves in mind. We employ the first order generalized harmonic gauge formulation. The relevant theory is reviewed…
In this paper, we initiate the rigorous mathematical study of the problem of impulsive gravitational spacetime waves. We construct such spacetimes as solutions to the characteristic initial value problem of the Einstein vacuum equations…
We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to…