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Singularities and the geometry of spacetime

The European Physical Journal H, 2014
The aim of this essay is to investigate certain aspects of the geometry of the spacetime manifold in the General Theory of Relativity with particular reference to the occurrence of singularities in cosmological solutions and their relation with other global properties. Section 2 gives a brief outline of Riemannian geometry.
Stephen Hawking
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Tolerance for spacetime singularities

Foundations of Physics, 1996
A common reaction to the Penrose-Hawking singularity theorems is that Einstein's general theory of relativity contains the seeds of its own destruction. This attitude is critically examined. A more tolerant attitude toward spacetime singularities is recommended.
John Earman, Earman John
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Spike behavior in the approach to spacetime singularities

Physical Review D, 2020
We perform numerical simulations of the approach to spacetime singularities. The simulations are done with sufficient resolution to resolve the small scale features (known as spikes) that form in this process.
David Garfinkle, Frans Pretorius
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Exploring Spacetime and Singularities [PDF]

, 2005
Master of Science (MSc)
Mamolo, Ami
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Fuchsian methods and spacetime singularities [PDF]

Classical and Quantum Gravity, 2004
Fuchsian methods and their applications to the study of the structure of spacetime singularities are surveyed. The existence question for spacetimes with compact Cauchy horizons is discussed. After some basic facts concerning Fuchsian equations have been
Alan D Rendall
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QUANTUM SINGULARITY OF QUASIREGULAR SPACETIMES

The Ninth Marcel Grossmann Meeting, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Konkowski, D. A., Helliwell, T. M.
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Strings falling into spacetime singularities

Physical Review D, 1992
We study the dynamics of strings near spacetime singularities. We consider gravitational-wave backgrounds with a singularity of the type {vert bar}{ital U}{vert bar}{sup {minus}{beta}}, {ital U} being a null coordinate. (The case with a {delta}({ital U}) shock-wave singularity turns out to be similar to the {beta}=1 case.) New features in the string ...
de Vega, Héctor J., Sánchez, Norma G.
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Strengths of singularities in Vaidya spacetimes

Physical Review D, 1987
The strengths of shell-focusing singularities in the ingoing Vaidya spacetimes are examined in terms of limiting focusing conditions. The singularities are found to be strong-curvature singularities only for mass functions which are initially linear functions of the advanced time.
, Rajagopal, , Lake
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On singularity-free spacetimes

Pramana, 1995
We consider here the metric for the singularity-free family of fluid models. The metric is unique for cylindrically symmetric space-time with metric potentials being separable functions of radial and time coordinates in the comoving coordinates. It turns out that fluid models separate out into two classes, withρ ≠µp in general butρ = 3p in particular ...
Naresh Dadhich, L K Patel, R Tikekar
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Singularities in spacetimes with torsion

International Journal of Theoretical Physics, 1990
The author briefly comments on the question of whether or not the Hawking-Penrose singularity theorems are affected by the introduction of torsion. To that end, the corresponding generalization of the Raychaudhuri equation is considered. The paper, however, chiefly consists in proposals of what should be done in future work.
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