相关论文: Spacetime singularities and curvature blow-ups

Spacetime singularities have been discovered which are physically much weaker than those predicted by the classical singularity theorems. Geodesics evolve through them and they only display infinities in the derivatives of their curvature…

The occurrence of singularities where spacetime curvature becomes infinite and geodesic evolution breaks down are inevitable events in classical general relativity (GR) unless one chooses an exotic matter violating weak energy condition.…

This work is an extensive literature review focusing on a few of the important topics in the large-scale structure of spacetime. The work is a Bachelor's thesis submitted at the Institute of Theoretical Physics, University of Leipzig. The…

The abstract boundary construction of Scott and Szekeres is a general and flexible way to define singularities in General Relativity. The abstract boundary construction also proves of great utility when applied to questions about more…

In this paper, we study rigidity aspects of Penrose's singularity theorem. Specifically, we aim to answer the following question: if a spacetime satisfies the hypotheses of Penrose's singularity theorem except with weakly trapped surfaces…

We present a review of the two prominent singularity theorems due to Penrose and Hawking, as well as their physical interpretation. Their usage is discussed in detail for the Schwarzschild spacetime with positive and negative mass. First,…

In this paper we present a proof of a mathematical version of the strong cosmic censor conjecture attributed to Geroch-Horowitz and Penrose but formulated explicitly by Wald. The proof is based on the existence of future-inextendible causal…

I investigate spacetime singularities from the point of view of the wavefunction of the universe. In order to extend the classical notion of geodesic incompleteness one has to include the proper time of an observer as a degree of freedom in…

Singularities in general relativity such as the big bang and big crunch, and exotic singularities such as the big rip are the boundaries of the classical spacetimes. These events are marked by a divergence in the curvature invariants and…

Recently many people have discussed the possibility that the universe is hyperbolic and was in an inflationary phase in the early stage. Under these assumptions, it is shown that the universe cannot have compact hyperbolic time-slices.…

We show that the absence of unbounded algebraic curvature invariants constructed from polynomials of the Riemann tensor cannot guarantee the absence of strong singularities. As a consequence, it is not sufficient to rely solely on the…

The global hyperbolicity assumption present in gravitational collapse singularity theorems is in tension with the quantum mechanical phenomenon of black hole evaporation. In this work I show that the causality conditions in Penrose's…

Using the standard Whitney topologies on spaces of Lorentzian metrics, we show that the existence of causal incomplete geodesics is a $C^\infty$-generic feature within the class of spacetimes of a given dimension $n\geq 3$ that are stably…

After the heroic epoch of Causality Theory, problems concerning the smoothability of time functions and Cauchy hypersurfaces remained as unanswered folk questions. Just recently solved, our aim is to discuss the state of the art on this…

We establish a new CMC (constant mean curvature) existence result for cosmological spacetimes, i.e., globally hyperbolic spacetimes with compact Cauchy surfaces satisfying the strong energy condition. If the spacetime contains an expanding…

Foliations by constant mean curvature hypersurfaces provide a possibility of defining a preferred time coordinate in general relativity. In the following various conjectures are made about the existence of foliations of this kind in…

The problem of a rigorous theory of singularities in space-times with torsion is addressed. We define geodesics as curves whose tangent vector moves by parallel transport. This is different from what other authors have done, because their…

We investigate the causal structure of $(1+1)$-dimensional spacetimes. For two sets of field equations we show that at least locally any spacetime is a solution for an appropriate choice of the matter fields. For the theories under…

We study the effects of trans-planckian censorship conjecture (TCC) bounds on geodesic completeness of spacetime and the associated existence for an infinite proper time. Using Gronwall's lemma, TCC bounds can be derived directly, leading…

In the mathematical physics literature, there are heuristic arguments, going back three decades, suggesting that for an open set of initially smooth solutions to the Einstein-vacuum equations in high dimensions, stable, approximately…