Regular coordinate systems for Schwarzschild and other spherical spacetimes

By K. Martel, E. Poisson. 2000

202 citations recorded by the source corpus.

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 Painleve–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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/972c965bdd3f5036697fec9903ca3a6b03a08f39

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In Applied Mathematics

1. Sam R. Dolan
2. Grigory E. Volovik

In Astronomy and Astrophysics

1. Sam R. Dolan
2. Hao Yang
3. Yang Guo
4. Grigory E. Volovik
5. Chen Lan
6. Y. Miao
7. Paolo Pani
8. V. Cardoso

In Statistical and Nonlinear Physics

1. Sam R. Dolan
2. Hao Yang
3. Yang Guo
4. Grigory E. Volovik
5. Chen Lan
6. Y. Miao

Citations in the corpus

• The Universe in a Helium Droplet (2003, background): “13) with Q = 0), the Painlevé–Gullstrand metric has many advantages (Kraus and Wilczek 1994; Parikh and Wilczek 2000; Martel and Poisson 2001; Schützhold 2001).”
• The river model of black holes (2004, unknown): “esian coordinates xµ = (x0,x1,x2,x3) = (t ff,x,y,z) instead of spherical coordinates: ds2 = η µν(dx µ −βµdt ff)(dx ν −βνdt ff) (8) where ηµν is the Minkowski metric, and βµ = β 0,− x r ,− y r ,− z r (9) are the components of the radial river velocity. Let gµ denote the basis of tangent vectors in the”
• Regular Black Holes: A Short Topic Review (2023, background): “For instance, the coordinate singularity of Hayward BHs [105] can be removed in the Painlevé-Gullstand coordinate system [216] and such a coordinate system is not unique, that is, the Kruskal-Szekeres coordinate and Eddington-Finkelstein coordinate systems [12] have the same effect.”
• Instability of the massive Klein-Gordon field on the Kerr spacetime (2007, methodology): “Let us begin by considering the Schwarzschild spacetime described by Painlevé-Gullstrand (PG) coordinates [36], ds(2) = (1 − 2M/r) dt(2) − √ 8M/rdtdr − dr(2) − dΩ(2) (A1) The contravariant metric tensor has components g = 1, g = − √ 2M/r and g = −(1 − 2M/r).”