Related papers: Linearized gravitational waves near space-like and…
We study semilinear wave equations with Ginzburg-Landau type nonlinearities multiplied by a factor $\epsilon^{-2}$, where $\epsilon>0$ is a small parameter. We prove that for suitable initial data, solutions exhibit energy concentration…
The periodic standing wave method studies circular orbits of compact objects coupled to helically symmetric standing wave gravitational fields. From this solution an approximation is extracted for the strong field, slowly inspiralling…
We present the first numerical simulations of asymptotically flat space-times whose computational domain includes past and future null-infinity. As an application, we explore the scattering of a gravitational wave in a black hole…
The NP constants of massless spin-0 fields propagating in Minkowski spacetime are computed close to spatial and null infinity by means of Friedrich's \emph{$i^0$-cylinder}. Assuming certain regularity condition on the initial data ensuring…
In this contribution we present an overview of our work on the numerical simulation of the perturbation of a black hole space-time by incoming gravitational waves. The formulation we use is based on Friedrich's general conformal equations…
We consider the global evolution problem for Einstein's field equations in the near-Minkowski regime and study the long-time dynamics of a massive scalar field evolving under its own gravitational field. We establish the existence of a…
Linear zero-rest-mass fields generically develop logarithmic singularities at the critical sets where spatial infinity meets null infinity. Friedrich's representation of spatial infinity is ideally suited to study this phenomenon. These…
Using a set of field equations in the null surface formulation we obtain the linearized coupling between the gravitational and matter fields. We first derive a formula for the metric of the space time and then we use this formula to study…
It has recently been demonstrated (Class. Quantum Grav. 31, 085010, 2014) that the conformally invariant wave equation on a Minkowski background can be solved with a fully pseudospectral numerical method. In particular, it is possible to…
The aim of these notes is to give an accessible and self-contained introduction to the theory of gravitational waves as the theory of a relativistic symmetric tensor field in a Minkowski background spacetime. This is the approach of a…
An important concept in Physics is the notion of an isolated system. It is used in many different areas to describe the properties of a physical system which has been isolated from its environment. The interaction with the `outside' is then…
The theory presented in this monograph establishes the first mathematically rigorous result on the global nonlinear stability of self-gravitating matter under small perturbations of an asymptotically flat, spacelike hypersurface of…
The spinorial version of the conformal vacuum Einstein field equations are used to construct a system of quasilinear wave equations for the various conformal fields. As a part of the analysis we also show how to construct a subsidiary…
We investigate the use of asymptotically null slices combined with stretching or compactification of the radial coordinate for the numerical simulation of asymptotically flat spacetimes. We consider a 1-parameter family of coordinates…
In this paper, we prove the nonlinear stability in exponential time of Minkowki space-time with a translation space-like Killing field. In the presence of such a symmetry, the 3 + 1 vacuum Einstein equations reduce to the 2 + 1 Einstein…
In this paper we prove the nonlinear stability of Minkowski space-time with a translation Killing field. In the presence of such a symmetry, the 3 + 1 vacuum Einstein equations reduce to the 2 + 1 Einstein equations with a scalar field. We…
The Conformal Einstein equations and the representation of spatial infinity as a cylinder introduced by Friedrich are used to analyse the behaviour of the gravitational field near null and spatial infinity for the development of data which…
In axial symmetry, there is a gauge for Einstein equations such that the total mass of the spacetime can be written as a conserved, positive definite, integral on the spacelike slices. This property is expected to play an important role in…
We make use of Friedrich's representation of spatial infinity to study asymptotic expansions of the Maxwell-scalar field system near spatial infinity. The main objective of this analysis is to understand the effects of the non-linearities…
We address the problem of deriving the post-Minkowskian approximation, widely used in current gravitational wave literature by investigating a possible deduction out of the recursive N\"other coupling approach, from the Pauli-Fierz spin-2…