5

Many books on special relativity eventually mention that the geometry of spacetime is special because the metric has a signature $(-,+,+,+)$ which is non-Euclidean. I have encountered many ways this makes it different from normal Euclidean geometry, for example, there is more than one null vector.

I want to study the mathematics of this new geometry in order to develop some intuition for it. I understand that the new geometry is called Hyperbolic geometry. Unfortunately, the information I find about that is all about negatively-curved saddles and Poincare disks, etc, which while interesting, seems quite different!

Can someone point to a good resource for learning just the geometry that underlies SR?

xuanji
  • 1,092

1 Answers1

4

The geometry of special relativity is called Lorentzian geometry, or in full: the "pseudo-Riemannian geometry of Minkowsk spacetime". This is also the Cartan geometry of the Lorentz group inside the Poincaré group.

See on the nLab at Lorentzian geometry for further pointers. See the References there for introductions and surveys.

Urs Schreiber
  • 14,227