Regular coordinate systems for Schwarzschild and other spherical spacetimes

Details Regular coordinate systems for Schwarzschild and other spherical spacetimes Regular coordinate systems for Schwarzschild and other spherical spacetimes

2000-01-22

arxiv.org/abs/gr-qc/0001069v4

Am.J.Phys. 69 (2001) 476-480

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages, 2 figures, ReVTeX; minor changes were made, new references were included

Scientific paper

10.1119/1.1336836

The continuation of the Schwarzschild metric across the event horizon is almost always (in textbooks) carried out using the Kruskal-Szekeres coordinates, in terms of which the areal radius r is defined only implicitly. We argue that from a pedagogical point of view, using these coordinates comes with several drawbacks, and we advocate the use of simpler, but equally effective, coordinate systems. One such system, introduced by Painleve and Gullstrand in the 1920's, is especially simple and pedagogically powerful; it is, however, still poorly known today. One of our purposes here is therefore to popularize these coordinates. Our other purpose is to provide generalizations to the Painleve-Gullstrand coordinates, first within the specific context of Schwarzschild spacetime, and then in the context of more general spherical spacetimes.

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