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)