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arXiv · 1211.4337

Coordinate families for the Schwarzschild geometry based on radial timelike geodesics

Tehani K. Finch
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Abstract

We explore the connections between various coordinate systems associated with observers moving inwardly along radial geodesics in the Schwarzschild geometry. Painlev\'e-Gullstrand (PG) time is adapted to freely falling observers dropped from rest from infinity; Lake-Martel-Poisson (LMP) time coordinates are adapted to observers who start at infinity with non-zero initial inward velocity; Gautreau-Hoffmann (GH) time coordinates are adapted to observers dropped from rest from a finite distance from the black hole horizon. We construct from these an LMP family and a proper-time family of time coordinates, the intersection of which is PG time. We demonstrate that these coordinate families are distinct, but related, one-parameter generalizations of PG time, and show linkage to Lema\^itre coordinates as well.

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Tehani K. Finch. 2012-11-19. Coordinate families for the Schwarzschild geometry based on radial timelike geodesics. https://doi.org/10.1007/s10714-015-1891-7

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