MG11 
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Relative strains in general relativity

The definition of relative accelerations and strains among a set of comoving particles is studied in connection with the geometric properties of the frame adpated to "fiducial observer." We find that a relativistically complete and correct definition of strains must account for the transport law of the chosen spatial triad along the observer's congruence and use special congruences of (accelerated) test particles in some familiar spacetimes to elucidate such point. The celebrated idea of Szekeres' compass of inertia, arising when studying geodesic deviation among a set of free-falling particles is then generalized to the case of accelerated particles and made observer and frame dependent, a fact that results of special interest when planning general relativistic tests on space stations orbiting around black holes and also in other gravitational situations, corresponding to different Petrov type of the background field.