Relativistic Gravity Gradiometry: The Mashhoon--Theiss Effect

TL;DR

This paper explores the measurement of relativistic tidal effects in Kerr spacetime, specifically analyzing the Mashhoon--Theiss effect, which arises from gravitomagnetic resonance phenomena in gravity gradiometry.

Contribution

It specializes Marck's general tidal matrix results to inclined circular orbits around rotating bodies, revealing the linear-order Mashhoon--Theiss effect due to gravitomagnetic resonance.

Findings

Recovery of the Mashhoon--Theiss effect in Kerr spacetime

Identification of a long-period gravitomagnetic component in the tidal matrix

Physical interpretation of the resonance phenomenon

Abstract

In general relativity, relativistic gravity gradiometry involves the measurement of the relativistic tidal matrix, which is theoretically obtained from the projection of the Riemann curvature tensor onto the orthonormal tetrad frame of an observer. The observer's 4-velocity vector defines its local temporal axis and its local spatial frame is defined by a set of three orthonormal nonrotating gyro directions. The general tidal matrix for the timelike geodesics of Kerr spacetime has been calculated by Marck\cite{Marck}. We are interested in the measured components of the curvature tensor along the inclined "circular" geodesic orbit of a test mass about a slowly rotating astronomical object of mass $M$ and angular momentum $J$. Therefore, we specialize Marck's results to such a "circular" orbit that is tilted with respect to the equatorial plane of the Kerr source. To linear order in $J$, we recover the Mashhoon--Theiss effect, which is due to a small denominator ("resonance") phenomenon involving the frequency of geodetic precession. The Mashhoon--Theiss effect shows up as a special long-period gravitomagnetic part of the relativistic tidal matrix. The physical interpretation of this effect is briefly discussed.