Schwarzschild Spacetime Under Generalised Gullstrand–Painlevé Slicing

  title={Schwarzschild Spacetime Under Generalised Gullstrand–Painlev{\'e} Slicing},
  author={Colin Maclaurin},
  journal={Einstein Equations: Physical and Mathematical Aspects of General Relativity},
  • C. Maclaurin
  • Published 16 May 2018
  • Physics
  • Einstein Equations: Physical and Mathematical Aspects of General Relativity
We investigate a foliation of Schwarzschild spacetime determined by observers freely falling in the radial direction. This is described using a generalisation of Gullstrand–Painleve coordinates which allows for any possible radial velocity. This foliation provides a contrast with the usual static foliation implied by Schwarzschild coordinates. The 3-dimensional spaces are distinct for the static and falling observers, so the embedding diagrams, spatial measurement, simultaneity, and time at… 

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