Near-horizon geodesics for astrophysical and idealised black holes: Coordinate velocity and coordinate acceleration
arXiv:1710.06139 · doi:10.3390/universe4060068
Abstract
Geodesics (by definition) have an intrinsic 4-acceleration zero. However, when expressed in terms of coordinates, the coordinate acceleration can very easily be non-zero, and the coordinate velocity can behave unexpectedly. The situation becomes extremely delicate in the near-horizon limit---for both astrophysical and idealised black holes---where an inappropriate choice of coordinates can quite easily lead to significant confusion. We shall carefully explore the relative merits of horizon-penetrating versus horizon-non-penetrating coordinates, arguing that in the near-horizon limit the coordinate acceleration is best interpreted in terms of horizon-penetrating coordinates.
V1: 25 pages, 10 figures. V2: Now 28 pages; slight change in title and abstract; some discussion and extra references added. Closely resembles published version
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