On-Axis Tidal Forces in Kerr Spacetime
arXiv:2003.09506
Abstract
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.
arXiv comment13 pages, 15 figures, accepted for publication in The European Physical Journal Plus
References in corpus (11)
- Scattering of scalar waves by rotating black holes
- Black hole tidal problem in the Fermi normal coordinates
- Absorption of electromagnetic and gravitational waves by Kerr black holes: Shadows, superradiance and the spin-helicity effect
- Massive and charged scalar field in Kerr-Newman spacetime: Absorption and superradiance
- On the instability for massive scalar fields in Kerr-Newman spacetime
- Analytic treatment of the system of a Kerr-Newman black hole and a charged massive scalar field
- Absorption of electromagnetic plane waves by rotating black holes
- Tidal Dynamics of Relativistic Flows Near Black Holes
- Scalar absorption by charged rotating black holes
- Relativistic Tidal Acceleration of Astrophysical Jets
- Kerr Geodesics Following the Axis of Symmetry