On-axis tidal forces in Kerr spacetime

Tidal forces are an important feature of general relativity, which are related to the curvature tensor. We analyze the tidal tensor in Kerr spacetime, with emphasis on the case along the symmetry axis of the Kerr black hole, noting that tidal forces may vanish at a certain point, unlike in the Schwa...

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Bibliographic Details
Published inEuropean physical journal plus Vol. 135; no. 3; p. 334
Main Authors Lima Junior, Haroldo C. D., Crispino, Luís C. B., Higuchi, Atsushi
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2020
Springer Nature B.V
Subjects
Applied and Technical Physics
Atomic
Black holes
Complex Systems
Condensed Matter Physics
Curvature
Event horizon
Geometry
Investigations
Mathematical analysis
Mathematical and Computational Physics
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
Relativity
Spacetime
Symmetry
Tensors
Theoretical
Tidal effects
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Summary:Tidal forces are an important feature of general relativity, which are related to the curvature tensor. We analyze the tidal tensor in Kerr spacetime, with emphasis on the case along the symmetry axis of the Kerr black hole, noting that tidal forces may vanish at a certain point, unlike in the Schwarzschild spacetime, using Boyer–Lindquist coordinates. We study in detail the effects of vanishing tidal forces in a body constituted of dust infalling along the symmetry axis. We find the geodesic deviation equations and solve them, numerically and analytically, for motion along the symmetry axis of the Kerr geometry. We also point out that the intrinsic Gaussian curvature of the event horizon at the symmetry axis is equal to the component along this axis of the tidal tensor there.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-020-00342-7