Related papers: Numerical calculations near spatial infinity
General relativistic Gauss equations for osculating elements for bound orbits under the influence of a perturbing force in an underlying Schwarzschild space-time have been derived in terms of Weierstrass elliptic functions. Thereby, the…
To numerically evolve the full Einstein equations (or modifications thereof), simulations of cosmological spacetimes must rely on a particular formulation of the field equations combined with a specific gauge/frame choice. Yet truly…
In this paper, we investigate the numerical solutions for spherically symmetric situations in Einstein cubic gravity. In addition to the previously found black hole solutions, we uncover a new class of solutions that lack horizons. Due to…
We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past…
We generate an explicit four-fold infinity of physically acceptable exact perfect fluid solutions of Einstein's equations by way of conformal transformations of physically unacceptable solutions (one way to view the use of isotropic…
The null string equations of motion and constraints in the Schwarzschild spacetime are given. The solutions are those of the null geodesics of General Relativity appended by a null string constraint in which the "constants of motion" depend…
For conformally invariant gravity theories defined on Riemannian spacetime and having the Schwarzschild--de-Sitter (SdS) metric as a solution in the Einstein gauge, we consider whether one may conformally rescale this solution to obtain…
The conformal structure of the Schwarzschild-de Sitter spacetime is analysed using the extended conformal Einstein field equations. To this end, initial data for an asymptotic initial value problem for the Schwarzschild-de Sitter spacetime…
We investigate the gravitational collapse of a massive scalar field in a conformally flat, spherically symmetric spacetime within general relativity. The collapsing matter distribution is modeled using a minimally coupled homogeneous scalar…
This is the first of a series of papers describing a numerical implementation of the conformally rescaled Einstein equation, an implementation designed to calculate asymptotically flat spacetimes, especially spacetimes containing black…
We derive a transformation of the noncommutative geometry inspired Schwarzschild solution into new coordinates such that the apparent unphysical singularities of the metric are removed. Moreover, we give the maximal singularity-free atlas…
The known canonical quantum theory of a spherically symmetric pure (Schwarzschild) gravitational system describes isolated black holes by plane waves exp(-iMc^2\tau/\hbar) with respect to their continuous masses M and the proper time \tau…
We provide a prescription to solve the metric completion problem in gravitational self-force calculations on a Kerr spacetime by fixing the remaining gauge freedom. We discuss the explicit example of eccentric equatorial orbits, recovering…
The Schwarzschild spacetime metric of negative mass is well-known to contain a naked singularity. In a spacelike slice, this singularity of the metric is characterized by the property that nearby surfaces have arbitrarily small area. We…
We investigate static spherically symmetric solutions within the framework of the local limit of nonlocal gravity. This theory departs from Einstein's general relativity (GR) through the introduction of a scalar gravitational susceptibility…
The well-known Schwarzschild black hole was first obtained as a stationary, spherically symmetric solution of the Einstein's vacuum field equations. But until thirty years later, efforts were made for the analytic extension from the…
We review and compare different computational variational methods applied to a system of fourth order equations that arises as a model of cylinder buckling. We describe both the discretization and implementation, in particular how to deal…
In this work, we study linearised gravitational fields on the entire Minkowski space-time including space-like infinity. The generalised conformal field equations linearised about a Minkowski background are utilised for this purpose. In…
We show that existing decay results for scalar fields on the Schwarzschild metric are sufficient to obtain a conformal scattering theory. Then we re-interpret this as an analytic scattering theory defined in terms of wave operators, with an…
We present an efficient numerical code based on spectral methods to integrate the field equations of general Robinson-Trautmann spacetimes. The most natural basis functions for the spectral expansion of the metric functions are spherical…