Regular Article - Theoretical Physics
When Painlevé–Gullstrand coordinates fail
Department of Physics and Astronomy, Bishop’s University, 2600 College Street, Sherbrooke, QC, J1M 1Z7, Canada
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Accepted: 12 August 2020
Published online: 25 August 2020
Painlevé–Gullstrand coordinates, a very useful tool in spherical horizon thermodynamics, fail in anti-de Sitter space and in the inner region of Reissner–Nordström. We predict this breakdown to occur in any region containing negative Misner–Sharp–Hernandez quasilocal mass because of repulsive gravity stopping the motion of PG observers, which are in radial free fall with zero initial velocity. PG coordinates break down also in the static Einstein universe for completely different reasons. The more general Martel-Poisson family of charts, which normally has PG coordinates as a limit, is reported for static cosmologies (de Sitter, anti-de Sitter and the static Einstein universe).
© The Author(s), 2020