Related papers: Analytic conformal compactification of Schwarzschi…
We consider a broad class of static, spherically symmetric generalized Schwarzschild-like solutions with multiple non-interacting anisotropic fluid sources and derive the coordinate transformation from Schwarzschild-like (curvature) to…
We interpret the lens transformation (a variant of the pseudoconformal transformation) as a pseudoconformal compactification of spacetime, which converts the nonlinear Schr\"odinger equation (NLS) without potential with a nonlinear…
In this article, we study the trajectory equations of the bounded radial geodesics in the generalized black-to-white hole bounce with mass difference and the Schwarzschild-to-de Sitter transition approximated by the thin-shell formalism. We…
We construct perturbations of Minkowski spacetime in general relativity, when given initial data that decays inverse polynomially to initial data of a Kerr spacetime towards spacelike infinity. We show that the perturbations admit a regular…
I derive a smooth and global Kruskal-Szekeres coordinate chart for the maximal extension of the non-extremal Reissner-Nordstr\"om geometry that provides a generalization to the standard inner and outer Kruskal-Szekeres coordinates. The…
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…
The Kruskal - Szekeres (KS) completion of the Schwarzschild spacetime is open to Synge's methodological criticism that the KS procedure generates "good" coordinates from "bad". This is addressed here in two ways: First I generate the KS…
We use the Kruskal time coordinate T to define the initial time. By this way, it naturally divides the stable study into one connected with the two regions: the white-hole-connected region and the black-hole-connected region. The union of…
We construct non-trivial vacuum space-times with a global Scri. The construction proceeds by proving extension results across compact boundaries for initial data sets, adapting the gluing arguments of Corvino and Schoen. Another application…
We present a detailed, mathematically rigorous description of the construction procedure of Penrose diagrams for the example of the maximal analytic extension of the exterior Schwarzschild spacetime. To this end, we first outline the…
Slice stretching effects such as slice sucking and slice wrapping arise when foliating the extended Schwarzschild spacetime with maximal slices. For arbitrary spatial coordinates these effects can be quantified in the context of boundary…
We present a class of spherically symmetric hypersurfaces in the Kruskal extension of the Schwarzschild space-time. The hypersurfaces have constant negative scalar curvature, so they are hyperboloidal in the regions of space-time which are…
The use of compactified hyperboloidal coordinates for metric formulations of the Einstein field Equations introduces formally singular terms in the equations of motion whose numerical treatment requires care. In this paper we study a…
The event horizon of the Schwarzschild black hole has been well studied and the singular behavior of the Schwarzschild metric on horizon is understood as a coordinate singularity rather than an essential singularity. One demonstration of…
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…
Generally, the Schwarzschild black hole was proved stable through two different methods: the mode-decomposition method and the integral method. In the paper, we show the integral method can only apply to the initial data vanishing at both…
The Schwarzschild geometry is investigated within the context of effective-field-theory models of gravity. Starting from its harmonic-coordinate expression, we derive the metric in standard coordinates by keeping the leading one-loop…
We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semi-classical theory. The singularity is eliminated but…
Using the synchronous coordinates, the creation of a Schwarzschild black hole immersed in a de Sitter spacetime can be viewed as a coherent creation of a collection of timelike geodesics. The previously supposed conical singularities do not…
In this pedagogical note, the Kruskal - Szekeres completion of the Schwarzschild spacetime is obtained explicitly in a few steps.