Tidal Dynamics in Kerr Spacetime

TL;DR

This paper analyzes the nonlinear tidal dynamics of test particles near Kerr black holes, revealing how relativistic speeds influence tidal acceleration and potential astrophysical phenomena.

Contribution

It introduces a transformed autonomous form of the generalized Jacobi equation for Kerr spacetime and explores tidal effects beyond critical speeds.

Findings

Particles launched vertically at speeds above c/√2 are tidally accelerated.

The nonlinear generalized Jacobi equation can be simplified to an autonomous form.

Results have potential applications in high-energy astrophysics.

Abstract

The motion of free nearby test particles relative to a stable equatorial circular geodesic orbit about a Kerr source is investigated. It is shown that the nonlinear generalized Jacobi equation can be transformed in this case to an autonomous form. Tidal dynamics beyond the critical speed c/sqrt(2) is studied. We show, in particular, that a free test particle vertically launched from the circular orbit parallel or antiparallel to the Kerr rotation axis is tidally accelerated if its initial relative speed exceeds c/sqrt(2). Possible applications of our results to high-energy astrophysics are briefly mentioned.