Critical Tidal Currents in General Relativity

TL;DR

This paper formulates relativistic tidal equations in Kerr spacetime, identifies critical tidal currents, and explores a tidal acceleration mechanism for test particles, advancing understanding of tidal effects in general relativity.

Contribution

It introduces a detailed analysis of relativistic tidal equations in Kerr spacetime, revealing critical tidal currents and a tidal acceleration mechanism.

Findings

Existence of relativistic critical tidal currents.

Analytic solutions of tidal equations in Kerr spacetime.

Identification of a tidal acceleration mechanism.

Abstract

Relativistic tidal equations are formulated with respect to the rest frame of a central gravitational source and their solutions are studied. The existence of certain relativistic critical tidal currents are thereby elucidated. 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 general tidal equations for the free motion of test particles are worked out with respect to the Kerr background. The analytic solutions of these equations are investigated and the existence of a tidal acceleration mechanism is emphasized.