Jacobi Fields and Tidal Effects in Kerr Spacetime

Abstract

General relativistic tidal equations are formulated with respect to the rest frame of a central gravitational source described by the Kerr gravitational field. Specifically, observers that are spatially at rest in the exterior Kerr spacetime are considered in detail; in effect, these fiducial observers define the rest frame of the Kerr source. The generalized Jacobi equation for the free motion of a test particle is worked out within the Fermi coordinate system established along the world line of a fiducial observer at rest on the symmetry axis of the exterior Kerr background. The nature of the solutions of these equations are investigated in connection with the phenomena associated with astrophysical jets.

arXiv comment27 pages, 5 figures

References in corpus (6)

• Fermi Coordinates for Weak Gravitational Fields
• Explicit Fermi Coordinates and Tidal Dynamics in de Sitter and Goedel Spacetimes
• Relativistic Tidal Acceleration of Astrophysical Jets
• Fermi coordinates in Schwarzschild spacetime: closed form expressions
• Fermi coordinates and static observer in Schwarzschild spacetime
• Physics in precision-dependent normal neighborhoods