Journal
UNIVERSE
Volume 4, Issue 6, Pages -Publisher
MDPI
DOI: 10.3390/universe4060068
Keywords
geodesic equation; coordinate velocity; coordinate acceleration; horizon-penetrating coordinates; horizon-non-penetrating coordinates
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Geodesics (by definition) have an intrinsic 4-acceleration zero. However, when expressed in terms of coordinates, the coordinate acceleration d(2)x(i) / dt(2) can very easily be non-zero, and the coordinate velocity dx(i) / dt 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 d(2)x(i) / dt(2) is best interpreted in terms of horizon-penetrating coordinates.
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