English

Lorentzian angles and trigonometry including lightlike vectors

General Relativity and Quantum Cosmology 2020-02-07 v2 High Energy Physics - Lattice High Energy Physics - Theory Mathematical Physics Differential Geometry math.MP

Abstract

We define a concept of Lorentzian angle that works even when one or both of the directions involved is null (lightlike). Such angles play a role in Regge-Calculus, in the boundary- and corner- terms for the gravitational action, and in the Lorentzian Gauss-Bonnet theorem (for which we provide a proof).

Cite

@article{arxiv.1908.10022,
  title  = {Lorentzian angles and trigonometry including lightlike vectors},
  author = {Rafael D. Sorkin},
  journal= {arXiv preprint arXiv:1908.10022},
  year   = {2020}
}

Comments

Version 2 has figures in final form. 39 pages, 12 figures. Most current version will be available at http://www.perimeterinstitute.ca/personal/rsorkin/some.papers/ (or wherever my home-page may be)

R2 v1 2026-06-23T10:57:36.393Z