相关论文: Fuchsian methods and spacetime singularities

We consider a class of Fuchsian equations that, for instance, describes the evolution of compressible fluid flows on a cosmological spacetime. Using the method of lines, we introduce a numerical algorithm for the singular initial value…

Spacetime singularities pose a long-standing puzzle in quantum gravity. Unlike Schwarzschild, a generic family of black holes gives rise to a Cauchy horizon on which, even in the Hartle-Hawking state, quantum observables such as $\langle…

This paper compares recent approaches appearing in the literature on the singularity problem for space-times with nonvanishing torsion.

This article presents a comprehensive and rigorous overview of spacetime singularities within the framework of classical General Relativity. Singularities are defined through the failure of geodesic completeness, reflecting the limits of…

Present knowledge about the nature of spacetime singularities in the context of classical general relativity is surveyed. The status of the BKL picture of cosmological singularities and its relevance to the cosmic censorship hypothesis are…

We equip the space of Cauchy hypersurfaces in a globally hyperbolic spacetime with a natural Hausdorff-type metric and study its properties, in particular completeness and local compactness, for Lorentzian manifolds and in more general…

A general geometrical scheme is presented for the construction of novel classical gravity theories whose solutions obey two-sided bounds on the sectional curvatures along certain subvarieties of the Grassmannian of two-planes. The…

We review recent efforts to construct gravitational theories on discrete space-times, usually referred to as the ``consistent discretization'' approach. The resulting theories are free of constraints at the canonical level and therefore…

The intention of this article is to give a flavour of some global problems in General Relativity. We cover a variety of topics, some of them related to the fundamental concept of 'Cauchy hypersurfaces': (1) structure of globally hyperbolic…

The most detailed existing proposal for the structure of spacetime singularities originates in the work of Belinskii, Khalatnikov and Lifshitz. We show rigorously the correctness of this proposal in the case of analytic solutions of the…

We present here a brief review and discussion on recent developments in the theory of spacetime singularities. After mentioning some key motivations on the main ideas and concepts involved, we take the approach that the singularities will…

We present some of the recent results and open questions on the causality problem in General Relativity. The concept of singularity is intimately connected with future trapped surface and inner event horizon formation. We offer a brief…

Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…

We study the near-horizon spacetime for isolated and dynamical trapping horizons (equivalently marginally outer trapped tubes). The metric is expanded relative to an ingoing Gaussian null coordinate and the terms of that expansion are…

In an earlier paper of the authors it was shown that the sheaf theoretically based recently developed abstract differential geometry of the first author can in an easy and natural manner incorporate singularities on arbitrary closed nowhere…

In this contribution, we study spacetimes of cosmological interest, without making any symmetry assumptions. We prove a rigid Hawking singularity theorem for positive cosmological constant, which sharpens known results. In particular, it…

The notion of singular generalized Finsler spacetime and singular generalized Berwald spacetime are introduced and their relevance for the description of classical gravity discussed. A method to construct examples of such generalized…

The Schwarzschild solution has played a fundamental conceptual role in general relativity, and beyond, for instance, regarding event horizons, spacetime singularities and aspects of quantum field theory in curved spacetimes. However, one…

Some examples from the mathematics of shape are presented that question some of the almost hidden assumptions behind results on limiting behaviour of finitary approximations to space-time. These are presented so as to focus attention on the…

This is a brief review article of a seminar given at the International Conference on Gravitation, Astrophysics and Cosmology 2024 (ICGAC-2024), Mathura, India. We begin with a historical survey of some singular solutions in the theory of…