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When Painlevé-Gullstrand coordinates fail.

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Painlevé-Gullstrand coordinates fail in anti-de Sitter and Reissner-Nordström spacetimes due to repulsive gravity. This breakdown, linked to negative quasilocal mass, also affects the static Einstein universe, necessitating alternative coordinate systems like Martel-Poisson charts.

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Area of Science:

  • General Relativity and Gravitational Physics
  • Theoretical Cosmology
  • Black Hole Thermodynamics

Background:

  • Painlevé-Gullstrand (PG) coordinates are essential for spherical horizon thermodynamics.
  • These coordinates are known to fail in specific non-standard spacetimes.
  • Understanding coordinate breakdown is crucial for accurate physical interpretations.

Purpose of the Study:

  • To identify regions where Painlevé-Gullstrand coordinates fail.
  • To explain the physical reasons behind the coordinate breakdown.
  • To introduce and analyze alternative coordinate systems for problematic spacetimes.

Main Methods:

  • Analysis of Painlevé-Gullstrand coordinate behavior in anti-de Sitter and Reissner-Nordström spacetimes.
  • Investigation of the role of negative Misner-Sharp-Hernandez quasilocal mass in coordinate breakdown.
  • Examination of coordinate behavior for observers in radial free fall.
  • Study of the static Einstein universe and the Martel-Poisson family of charts.

Main Results:

  • Painlevé-Gullstrand coordinates fail in anti-de Sitter space and the inner Reissner-Nordström region.
  • Coordinate breakdown is predicted for any region with negative Misner-Sharp-Hernandez quasilocal mass due to repulsive gravity.
  • The static Einstein universe exhibits PG coordinate breakdown for distinct reasons.
  • The Martel-Poisson family of charts, encompassing PG coordinates, is presented for static cosmologies.

Conclusions:

  • Repulsive gravity associated with negative quasilocal mass fundamentally limits the applicability of Painlevé-Gullstrand coordinates.
  • Alternative coordinate systems, such as the Martel-Poisson charts, are necessary for describing static cosmologies where PG coordinates fail.
  • The study clarifies the conditions and reasons for coordinate breakdown in diverse gravitational scenarios.