2000/01/31 by Karl Martel, Eric Poisson · 6 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.1119/1.1336836
published as Am.J.Phys. 69 (2001) 476-480 · 5 pages, 2 figures, ReVTeX; minor changes were made, new references were included
arxiv created 2000/10/18 · openalex publication_date 2001/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The continuation of the Schwarzschild metric across the event horizon is a well-understood problem discussed in most textbooks on general relativity. Among the most popular coordinate systems that are regular at the horizon are the Kruskal–Szekeres and Eddington–Finkelstein coordinates. Our first objective in this paper is to popularize another set of coordinates, the Painlevé–Gullstrand coordinates. These were first introduced in the 1920s, and have been periodically rediscovered since; they are especially attractive and pedagogically powerful. Our second objective is to provide generalizations of these coordinates, first within the specific context of Schwarzschild spacetime, and then in the context of more general spherical spacetimes.