In the q-metric, tidal stretching and compression of radially falling test particles depend on the deformation parameter q and the polar angle θ, and differ from Schwarzschild near the singularity at r=2m.
Tidal indicators in the spacetime of a rotating deformed mass
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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.
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Geodesic deviation in the $q$-metric
In the q-metric, tidal stretching and compression of radially falling test particles depend on the deformation parameter q and the polar angle θ, and differ from Schwarzschild near the singularity at r=2m.