Relativity and Singularities - A Short Introduction for Mathematicians

Abstract

We summarize the main ideas of General Relativity and Lorentzian geometry, leading to a proof of the simplest of the celebrated Hawking-Penrose singularity theorems. The reader is assumed to be familiar with Riemannian geometry and point set topology.

22 pages, 6 figures; v2: a few typos corrected; v3: more typos corrected; v4: proof of Theorem 3.13 fixed, figure added; v5: more typos corrected

Cited by in corpus (6)

• Editorial for the Special Issue 100 Years of Chronogeometrodynamics: The Status of the Einstein's Theory of Gravitation in Its Centennial Year
• Hawking's singularity theorem for $C^{1,1}$-metrics
• The adventures of Spacetime
• Entropy growth in the early universe and confirmation of initial big bang conditions (Why the quark-gluon model is not the best analogy)
• Sub-Lorentzian Geometry on Anti-De Sitter Space
• Shape maps for second order partial differential equations