Hyperboloidal

I demonstrate the hyperboloidal compactification method for numerically solving wave equations on unbounded domains. Animations and code included!

The last three papers by Charles W. Misner were about the hyperboloidal approach. This post is a short review of these papers motivated by the Misner Memorial Symposium on November 11, 2023.

Hyperboloidal hypersurfaces split spacetime into space and time. Their mathematical definition connects to a physical principle that may be useful as a mental image for the quantum foam.

This is the first installment of a three-piece series on Penrose diagrams and the associated conformal compactification procedure. This post is a technical how-to describing how I draw quantitatively accurate Penrose diagrams to illustrate the causal structure of time surfaces using free and open-source software.

Hyperbolic geometry provides a natural setting for special relativity. This viewpoint simplifies calculations, provides insights into the theory, and has applications beyond special relativity in machine learning and general relativity.

Minkowski spacetime in hyperboloidal coordinates takes the form of a stack of hyperbolic manifolds with the same spatial geometry as anti-de Sitter spacetime. Is there a hyperboloidal realization of holography for isolated systems?

Infinity may be closer than you think.