Tidal indicators in the spacetime of a rotating deformed mass

TL;DR

This paper investigates observer-dependent tidal effects in the spacetime of a rotating deformed mass, extending previous Kerr analyses by including matter with an arbitrary quadrupole moment and exploring related curvature invariants.

Contribution

It introduces a generalized background spacetime with quadrupole deformation and analyzes associated tidal indicators, curvature invariants, and super-energy quantities.

Findings

Tidal indicators depend on observer motion and quadrupole deformation.

Relations between tidal effects and curvature invariants are established.

Observer-dependent super-energy densities and Poynting vectors are characterized.

Abstract

Tidal indicators are commonly associated with the electric and magnetic parts of the Riemann tensor (and its covariant derivatives) with respect to a given family of observers in a given spacetime. Recently, observer-dependent tidal effects have been extensively investigated with respect to a variety of special observers in the equatorial plane of the Kerr spacetime. This analysis is extended here by considering a more general background solution to include the case of matter which is also endowed with an arbitrary mass quadrupole moment. Relation with curvature invariants and Bel-Robinson tensor, i.e., observer-dependent super-energy density and super-Poynting vector, are investigated too.