Related papers: Analytic conformal compactification of Schwarzschi…
Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat near infinity, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through…
The total spacetime manifold for a Schwarzschild black hole (BH) is described by the Kruskal coordinates u=u(r,t) and v=v(r,t), where r and t are the conventional Schwarzschild radial and time coordinates respectively. The relationship…
This article presents a streamlined version of the author's original proof of the $C^0$-inextendibility of the maximal analytic Schwarzschild spacetime. Firstly, we deviate from the original proof by using the result, recently established…
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…
Trumpet geometries play an important role in numerical simulations of black hole spacetimes, which are usually performed under the assumption of asymptotic flatness. Our Universe is not asymptotically flat, however, which has motivated…
Self-dual black holes in (2,2) signature spacetime -- Klein space -- have recently attracted interest in the context of celestial holography. Motivated by this development, we investigate the structure of spacetime near the horizons of…
We study the numerical propagation of waves through future null infinity in a conformally compactified spacetime. We introduce an artificial cosmological constant, which allows us some control over the causal structure near null infinity.…
The case of asymptotic Minkowskian space-times is considered. A special class of asymptotic rectilinear coordinates at the spatial infinity, related to a specific system of free falling observers, is chosen. This choice is applied in…
We develop a method for deriving approximate analytical formulae to integrate photon geodesics in a Schwarzschild spacetime. Based on this, we derive the approximate equations for light bending and propagation delay that have been…
We consider the problem of extending a conformal metric of negative curvature, given outside a neighbourhood of 0 in the unit disk $\DD$, to a conformal metric of negative curvature in $\DD$. We give conditions under which such an extension…
We study proper time ($\tau$) intervals for observers at rest in the universe ($U$) and anti-universe ($\bar{U}$) sectors of the Kruskal-Schwarzschild eternal spacetime of mass $M$, and proper lengths ($\rho$) in the black hole (BH) and…
We show that the Novikov coordinates can be obtained in a direct and physically transparent way from the radial geodesics of massive particles with negative energy in the Schwarzschild spacetime. These geodesics form a complete congruence…
The maximal analytic Schwarzschild spacetime is manifestly inextendible as a Lorentzian manifold with a twice continuously differentiable metric. In this paper, we prove the stronger statement that it is even inextendible as a Lorentzian…
Using the standard Cayley transform and elementary tools it is reiterated that the conformal compactification of the Minkowski space involves not only the "cone at infinity" but also the 2-sphere that is at the base of this cone. We…
We use the phenomenological approach to study properties of space-time in the vicinity of the Schwarzschild black-hole singularity. Requiring finiteness of the Schwarzschild-like metrics we come to the notion of integrable singularity that…
We discuss different kinds of Killing horizons possible in static, spherically symmetric configurations and recently classified as "usual", "naked" and "truly naked" ones depending on the near-horizon behavior of transverse tidal forces…
In the early 20th century, Laurent Schwartz observed that we can identify functions that extend smoothly to the point at infinity of one-point compactifications of Euclidean spaces. We show a similar result for a different compactification…
We determine the corrections to the Schwarzschild geometry arising from including the Goroff- Sagnotti counterterm in the gravitational dynamics. We find that static, asymptotically flat, and spherically symmetric geometries are completely…
Action-angle coordinates are a tool commonly used in celestial mechanics to systematically parametrize and store general solutions of the equations of motion of astrophysical bodies. I perturbatively construct action-angle coordinates for…
A framework conceptually based on the conformal techniques employed to study the structure of the gravitational field at infinity is set up in the context of loop quantum gravity to describe asymptotically anti-de Sitter quantum spacetimes.…