TL;DR
This paper discusses the theoretical framework of gravity gradiometry in general relativity, focusing on measuring tidal effects and the behavior of curvature components, including gravitomagnetic effects around rotating masses.
Contribution
It provides a detailed theoretical analysis of relativistic gravity gradiometry, including tidal matrix measurement, behavior under Lorentz boosts, and gravitomagnetic effects in rotating gravitational fields.
Findings
Analysis of tidal matrix measurement in relativistic settings
Description of curvature tensor behavior under Lorentz boosts
Elucidation of gravitomagnetic beat effects around rotating masses
Abstract
Gravity gradiometry within the framework of the general theory of relativity involves the measurement of the elements of the relativistic tidal matrix, which is theoretically obtained via the projection of the spacetime curvature tensor upon the nonrotating orthonormal tetrad frame of a geodesic observer. The behavior of the measured components of the curvature tensor under Lorentz boosts is briefly described in connection with the existence of certain special tidal directions. Relativistic gravity gradiometry in the exterior gravitational field of a rotating mass is discussed and a gravitomagnetic beat effect along an inclined spherical geodesic orbit is elucidated.
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