Observer-dependent tidal indicators in the Kerr spacetime

TL;DR

This paper investigates how different observers in Kerr spacetime perceive tidal effects, introducing observer-dependent tidal indicators and analyzing their behavior for various observer families, revealing unique measurement properties.

Contribution

It introduces and analyzes observer-dependent tidal indicators in Kerr spacetime, detailing their transformation laws and specific behaviors for stationary rotating and Carter's observers.

Findings

No equatorial circularly rotating observer measures zero tidal electric indicator.

Carter's observers measure zero tidal magnetic indicator.

Transformation laws relate tidal indicators between different observers.

Abstract

The observer-dependent tidal effects associated with the electric and magnetic parts of the Riemann tensor with respect to an arbitrary family of observers are discussed in a general spacetime in terms of certain "tidal indicators." The features of such indicators are then explored by specializing our considerations to the family of stationary circularly rotating observers in the equatorial plane of the Kerr spacetime. There exist a number of observer families which are special for several reasons and for each of them such indicators are evaluated. The transformation laws of tidal indicators when passing from one observer to another are also discussed, clarifying the interplay among them. Our analysis shows that no equatorial plane circularly rotating observer in the Kerr spacetime can ever measure a vanishing tidal electric indicator, whereas the family of Carter's observers measures zero tidal magnetic indicator.