Related papers: Curvature singularities and abstract boundary sing…
The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential…
Singularities play an important role in General Relativity and have been shown to be an inherent feature of most physically reasonable space-times. Despite this, there are many aspects of singularities that are not qualitatively or…
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…
The abstract boundary construction of Scott and Szekeres provides a `boundary' for any n-dimensional, paracompact, connected, Hausdorff, smooth manifold. Singularities may then be defined as objects within this boundary. In a previous paper…
At first we introduce the space-time manifold and we compare some aspects of Riemannian and Lorentzian geometry such as the distance function and the relations between topology and curvature. We then define spinor structures in general…
Singularity theorems of general relativity utilize the notion of causal geodesic incompleteness as a criterion of the presence of a spacetime singularity. The incompleteness of a causal curve implies the end and/or beginning of the…
The singularity theorems of Penrose, Hawking, and Geroch predict the existence of incomplete inextendible causal geodesics in a wide range of physically adequate spacetimes modeling the gravitational collapse of stars and the expanding…
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…
In this short paper, Penrose's famous singularity theorem is applied to the Kerr space-time. In the case of the maximally extended space-time, the assumptions of Penrose's singularity theorem are not satisfied as the space-time is not…
A new definition of a strong curvature singularity is proposed. This definition is motivated by the definitions given by Tipler and Krolak, but is significantly different and more general. All causal geodesics terminating at these new…
It has previously been shown [W. Rudnicki, Phys. Lett. A 224, 45 (1996)] that a generic gravitational collapse cannot result in a naked singularity accompanied by closed timelike curves. An important role in this result plays the so-called…
The classical singularity theorems of R. Penrose and S. Hawking from the 1960s show that, given a pointwise energy condition (and some causality as well as initial assumptions), spacetimes cannot be geodesically complete. Despite their…
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…
Following a survey of the abstract boundary definition of Scott and Szekeres, a rigidity result is proved for the smooth case, showing that the topological structure of the regular part of this boundary in invariantly defined.
A spacetime singularity, identified by the existence of incomplete causal geodesics in the spacetime, is called a (Tipler) strong curvature singularity if the volume form acting on independent Jacobi fields along causal geodesics vanishes…
Singularity theorems demonstrate the inevitable breakdown of the concept of continuous, classical spacetime under highly general conditions. Quantum gravity is expected to intervene to avoid singularities and models so far hint towards…
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…
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 causal boundary construction of Geroch, Kronheimer, and Penrose has some universal properties of importance for general studies of spacetimes, particularly when equipped with a topology derived from the causal structure. Properties of…
Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which,…