Beyond Schwarzschild: New Pulsating Coordinates for Spherically Symmetric Metrics
arXiv:2405.00278 · doi:10.1007/s10714-024-03218-8
Abstract
Starting from a general transformation for spherically symmetric metrics where g\_11=-1/g\_00, we analyze coordinates with the common property of conformal flatness at constant solid angle element. Three general possibilities arise: one where tortoise coordinate appears as the unique solution, other that includes Kruskal-Szekeres coordinates as a very specific case, but that also allows other similar transformations, and finally a new set of coordinates with very different properties than the other two. In particular, this represents any causal patch of the spherically symmetric metrics in a compactified form. We analyze some relations, taking the Schwarzschild case as prototype, but also contrasting the cosmological de-Sitter and Anti-de-Sitter solutions for the new proposed pulsating coordinates.
17 pages, 4 figures. Preliminar result was presented in GRG23 Conference (China, 2022). Find the published version (DOI below), improving interpretations and a result about AdS Spacetime in: https://rdcu.be/dz1ftrdcu.be/dz1ft
References in corpus (6)
- When is g_{tt} g_{rr} = -1?
- Cosmological Redshift in FRW Metrics with Constant Spacetime Curvature
- Horizons vs. singularities in spherically symmetric space-times
- Maximal extension of the Schwarzschild metric: From Painlevé-Gullstrand to Kruskal-Szekeres
- Kruskal coordinates as canonical variables for Schwarzschild black holes
- Regular frames for spherically symmetric black holes revisited