Related papers: Does asymptotic simplicity allow for radiation nea…
We prove Asymptotic Completeness of one dimensional NLS with long range nonlinearities. We also prove existence and expansion of asymptotic solutions with large data at infinity.
Asymptotically flat spacetimes have been studied in five separate regions: future/past timelike infinity $i^\pm$, future/past null infinity $\mathcal{I}^\pm$, and spatial infinity $i^0$. We formulate assumptions and definitions such that…
Shear-free or asymptotically shear-free null geodesic congruences possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant affects. It…
We construct the phase space of 3-dimensional asymptotically flat spacetimes that forms the bulk metric representation of the BMS group consisting of both supertranslations and superrotations. The asymptotic symmetry group is a unique copy…
A new method to visualize the curvature of spacetime was recently proposed. This method finds the eigenvectors of the "electric" and "magnetic" components of the Weyl tensor and, in analogy to the field lines of electromagnetism, uses the…
We analyse the asymptotic symmetries of Maxwell theory at spatial infinity through the Hamiltonian formalism. Precise, consistent boundary conditions are explicitly given and shown to be invariant under asymptotic angle-dependent…
On any asymptotically-flat spacetime, we show that the asymptotic symmetries and charges of Maxwell fields on past null infinity can be related to those on future null infinity as recently proposed by Strominger. We extend the covariant…
The directional behavior of dominant components of algebraically special spin-s fields near a spacelike, timelike or null conformal infinity is studied. By extending our previous general investigations we concentrate on fields which admit a…
We study spherically symmetric configurations of the quadratic $f(R)$ gravity in the Einstein frame. In case of a purely gravitational system, we have determined the global qualitative behavior of the metric and the scalaron field for all…
We consider a family of cylindrical spacetimes endowed with angular momentum that are solutions to the vacuum Einstein equations outside the symmetry axis. This family was recently obtained by performing a complete gauge fixing adapted to…
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…
The concepts of Lorentz invariance of local (flat space) physics, and unitarity of time evolution and the S-matrix, are famously rigid and robust, admitting no obvious consistent theoretical deformations, and confirmed to incredible…
We show the existence of the full compound asymptotics of solutions to the scalar wave equation on long-range non-trapping Lorentzian manifolds modeled on the radial compactification of Minkowski space. In particular, we show that there is…
The construction of the cylinder at spatial infinity for stationary spacetimes is considered. Using a specific conformal gauge and frame, it is shown that the tensorial fields associated to the conformal Einstein field equations admit…
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…
The asymptotic behavior of expanding, generic, $T^2$-Symmetric, vacuum spacetimes is examined via numerical simulations. After validation of the numerical methods, the properties of these generic spacetimes are explored and compared to…
This is the third paper in a series describing a numerical implementation of the conformal Einstein equation. This paper describes a scheme to calculate (three) dimensional data for the conformal field equations from a set of free…
We resume former discussions of the conformally invariant wave equation on a Schwarzschild background, with a particular focus on the behaviour of solutions near the 'cylinder', i.e. Friedrich's representation of spacelike infinity. This…
We show that the asymptotic charges associated with Lorentz symmetries on past and future null infinity match in the limit to spatial infinity in a class of asymptotically-flat spacetimes. These are spacetimes that obey the Ashtekar-Hansen…
We present new numerical cosmological solutions of the Einstein Field Equations. The spacetime is spherically symmetric with a source of dust and radiation approximated as a perfect fluid. The dust and radiation are necessarily non-comoving…