The Space of Causal Diamonds as a Lorentzian Pre-Length Space

Explore the geometry of causal diamonds in Mathematical Relativity through this 41-minute conference talk from the Workshop on "Non-regular Spacetime Geometry" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the unexplored structure of causal diamonds in spacetime and their potential for studying stability results associated with metric convergence. Learn how the hyperspace of causal diamonds in a Lorentzian product can be endowed with a Lorentzian pre-length space structure. Discover the global hyperbolicity of this space for complete S and gain insights into a family of its maximal timelike curves. Examine the relationship between this hyperspace and a Lorentzian uniform product through a distance and 1-homothety map. This talk presents joint work with W. Barrera and L. Montes, offering a comprehensive look at the application of synthetic methods inspired by metric geometry in Relativity.