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When Painlev\'e-Gullstrand coordinates fail

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arxiv 2006.10827 v2 pith:HPI7ZSCF submitted 2020-06-18 gr-qc

classification gr-qc
keywords coordinatessitterstaticanti-dee-gullstrandeinsteinfailpainlev
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Painlev\'e-Gullstrand coordinates, a very useful tool in spherical horizon thermodynamics, fail in anti-de Sitter space and in the inner region of Reissner-Nordstr\"om. 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 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).

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Cited by 2 Pith papers

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    gr-qc 2025-01 accept novelty 5.0 of 10

    The causal structure of black holes, including horizons and interiors, can be encoded in wind-Finsler metrics whose shifted indicatrices track null geodesics.

  2. Forces parallel to particle trajectories in relativistic gravity

    gr-qc 2025-07 reject novelty 2.0 of 10

    A pedagogical note claims that parallel forces in cosmology and scalar-tensor gravity can be reparametrized away, but its claim that such forces occur generally in Einstein frame scalar-tensor gravity relies on an inv...

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