Causality and Spacetimes 2022

Instructor: Ivo Terek.

Syllabus: The mini-course has three parts.

  1. Brief review of linear algebra on pseudo-Euclidean vector spaces. Conditions for the existence of a Lorentz metric on a smooth manifold. Existence and uniqueness of the time-orientable double-cover of a Lorentz manifold.
  2. Spacetimes and examples (Minkowski, Schwarzschild, Reissner-Nordström, FLRW). Chronological, causal, and horismos precedence relations, and some basic properties.
  3. Local causality and the push-up lemma. Future and past sets. Achronal boundaries and edge points.

Schedule: We will have three lectures per week, on Mondays, Wednesdays, and Fridays, from 2 p.m. to 3 p.m., starting on June 27th, and ending on July 15th, in room MW154. We also have a Zoom link for online attendance.

Main reference: Mainly chapter 3 of my book draft with Paolo Piccione (which we’ll share with the participants). Any feedback and corrections will be much appreciated.

Recordings and weekly notes:

Extra references:

  • O’Neill, B.; Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics, 103. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. xiii+468 pp. ISBN: 0-12-526740-1.
  • Penrose, R.; Techniques of differential topology in relativity. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 7. Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1972. viii+72 pp.
  • Beem, J. K.; Ehrlich, P. E.; Easley, K. L; Global Lorentzian geometry. Second edition. Monographs and Textbooks in Pure and Applied Mathematics, 202. Marcel Dekker, Inc., New York, 1996. xiv+635 pp. ISBN: 0-8247-9324-2.