Related papers: Static vacuum solutions from convergent null data …
It is shown that solutions to Einstein's field equations with positive cosmological constant can include non-zero rest-mass fields which coexist with and travel unimpeded across a smooth conformal boundary. This is exemplified by the…
This article is focused on the asymptotic expansions, as time tends to infinity, of solutions of a system of ordinary differential equations with non-smooth nonlinear terms. The forcing function decays to zero in a very complicated but…
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…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of…
We develop a framework for understanding the existence of asymptotically flat solutions to the static vacuum Einstein equations with prescribed boundary data consisting of the induced metric and mean curvature on a 2-sphere. A partial…
We demonstrate that in constructing asymptotically flat vacuum initial data sets in General Relativity via the conformal method, certain asymptotic structures may be prescribed a priori through the specified seed data, including the ADM…
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…
A complete characterization is obtained of the asymptotic behavior of solutions of the static vacuum Einstein equations which have a (pseudo)-compact horizon or boundary and are complete away from the boundary. It is proved that the…
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
We consider the Einstein-dust equations with positive cosmological constant $\lambda$ on manifolds with time slices diffeomorphic to an orientable, compact 3-manifold $S$. It is shown that the set of standard Cauchy data for the…
We obtain existence and local uniqueness of asymptotically flat, static vacuum extensions for Bartnik data on a sphere near the data of a sphere of symmetry in a Schwarzschild manifold.
This article uses the conformal Einstein equations and the conformal representation of spatial infinity introduced by Friedrich to analyse the behaviour of the gravitational field near null and spatial infinity for the development of…
We present an axially symmetric, asymptotically flat empty space solution of the Einstein field equations containing a naked singularity. The spacetime is regular everywhere except on the symmetry axis where it possess a true curvature…
We investigate circularly symmetric static solutions in three-dimensional gravity with a minimally coupled massive scalar field. We integrate numerically the field equations assuming asymptotic flatness, where black holes do not exist and a…
We prove the existence of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers…
In this paper, we consider the asymptotic profiles of zero points for the spatial variable of the solutions to the heat equation. By giving suitable conditions for the initial data, we prove the existence of zero points by extending the…
A study of the linearised gravitational field (spin 2 zero-rest-mass field) on a Minkowski background close to spatial infinity is done. To this purpose, a certain representation of spatial infinity in which it is depicted as a cylinder is…
We study the asymptotics of solutions to a particular class of systems of linear wave equations, namely, of silent equations. We obtain asymptotic estimates of all orders for the solutions, and show that solutions are uniquely determined by…
We use conformal geometry methods and the construction of Friedrich's cylinder at spatial infinity to study the propagation of spin-$0$ fields (solutions to the wave equation) on $n$-dimensional Minkowski spacetimes in a neighbourhood of…