IWARA2026 - 12th International Workshop on Astronomy and Relativistic Astrophysics

Representations of Spacetime: From Kruskal Coordinates and Stereographic Projections to Causal Diamonds and the Golden representation

Not scheduled

20m

Auditorio José Adem, Mexico

Talk

Speaker

Edgar Alejandro León Espinoza (Universidad Autónoma de Sinaloa)

Description

We start by examining the relations between the Kruskal representation and stereographic projection. Motivated by novel results in spherically-symmetric metrics, we explore the analogue of conformal-Minkowski mappings. To this end, we introduce 'Diamond Coordinates,' a compactified representation that naturally delineates local causal diamonds. By analyzing the worldlines of observers within finite interaction regions, we demonstrate how this framework explicitly captures the divergence of the Unruh temperature at the causal horizon. We conclude by mentioning another interesting recent development for these spacetimes, particularly the Schwarzschild black hole: the Golden representation, where the Golden Ratio appears to be ubiquitous.