Related papers: Some Remarks on the $C^0$-(in)extendibility of Spa…
Starting from the proof of the $C^0$-inextendibility of Schwarzschild by Sbierski, the past decade has seen renewed interest in showing low-regularity inextendibility for known spacetime models. Specifically, a lot of attention has been…
Utilizing some of Sbierski's recent $C^0$-inextendibility techniques [18], we prove the $C^0$-inextendibility of a class of spatially flat FLRW spacetimes without particle horizons.
This paper studies the singularity structure of FLRW spacetimes without particle horizons at the $C^0$-level of the metric. We show that in the case of constant spatial curvature $K=+1$, and without any further assumptions on the scale…
The Kasner spacetime is a cosmological model of an anisotropic expanding universe without matter and is an exact solution of the Einstein vacuum equations Ric(g) = 0. It is manifestly inextendible as a Lorentzian manifold with a twice…
Milne-like spacetimes are a class of FLRW models which admit $C^0$ spacetime extensions through the big bang. The boundary of a Milne-like spacetime can be identified with a null cone in the extension. We find that the comoving observers…
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…
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 paper investigates the structure of gravitational singularities at the level of the connection. We show in particular that for FLRW spacetimes with particle horizons a local holonomy, which is related to a gravitational energy, becomes…
We examine the $C^{0}$-formulation of the strong cosmic censorship conjecture (SCC) from a quantum complexity-theoretic perspective and argue that for generic black hole parameters as initial conditions for the Einstein equations,…
We reconsider space-time singularities in classical Einsteinian general relativity: with the help of several new co-ordinate systems we show that the Schwarzschild solution can be extended beyond the curvature singularity at r=0. The…
This is the first and main paper of a two-part series, in which we prove the $C^{2}$-formulation of the strong cosmic censorship conjecture for the Einstein-Maxwell-(real)-scalar-field system in spherical symmetry for two-ended…
It is a well-known fact that the Schwarzschild spacetime admits a maximal spacetime extension in null coordinates which extends the exterior Schwarzschild region past the Killing horizon, called the Kruskal-Szekeres extension. This method…
Milne-like spacetimes are a class of $k = -1$ FLRW spacetimes which admit continuous spacetime extensions through the big bang. In a previous paper [30], it was shown that the cosmological constant appears as an initial condition for…
Milne-like spacetimes are a class of hyperbolic FLRW spacetimes which admit continuous spacetime extensions through the big bang, $\tau = 0$. The existence of the extension follows from writing the metric in conformal Minkowskian…
Motivated by weak null singularities in black hole interiors, we study 1+1 dimensional Lorentzian manifolds $(M,g)$ which admit a continuous spacetime extension across a null boundary $v=0$, where $v<0$ is a null coordinate. We study the…
We study past-directed extendibility of Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) and Bianchi type I spacetimes with a scale factor vanishing in the past. We give criteria for determining whether a boundary for past-directed incomplete…
Imposing extendibility on Kasner-Fronsdal black hole local isometric embedding is equivalent to removing conic singularities in Kruskal representation. Allowing for globally non-trivial (living in $M_{5}\times S_{1}$) embeddings,…
Observational evidence, together with practical computations and modeling, supports a Euclidean spatial sector in the current cosmological model based on the FLRW metric. This, however, would imply that the total amount of matter and energy…
Given an extendible spacetime one may ask how much, if any, uniqueness can in general be expected of the extension. Locally, this question was considered and comprehensively answered in a recent paper of Sbierski, where he obtains local…
We show that the big bang is a coordinate singularity for a large class of $k = -1$ inflationary FLRW spacetimes which we have dubbed 'Milne-like.' By introducing a new set of coordinates, the big bang appears as a past boundary of the…