Strains in General Relativity

Abstract

The definition of relative accelerations and strains among a set of comoving particles is studied in connection with the geometric properties of the frame adapted to a "fiducial observer." We find that a relativistically complete and correct definition of strains must take into account the transport law of the chosen spatial triad along the observer's congruence. We use special congruences of (accelerated) test particles in some familiar spacetimes to elucidate such a point. The celebrated idea of Szekeres' compass of inertia, arising when studying geodesic deviation among a set of free-falling particles, is here generalized to the case of accelerated particles. In doing so we have naturally contributed to the theory of relativistic gravity gradiometer. Moreover, our analysis was made in an observer-dependent form, a fact that would be very useful when thinking about general relativistic tests on space stations orbiting compact objects like black holes and also in other interesting gravitational situations.

25 pages, 7 figures; published version

References in corpus (7)

• The Many Faces of Gravitoelectromagnetism
• A new form of the Kerr solution
• The Frenet Serret Description of Gyroscopic Precession
• The Generalized Jacobi Equation
• Ultrarelativistic Motion: Inertial and Tidal Effects in Fermi Coordinates
• Tidal Dynamics in Kerr Spacetime
• A Gravitational Mechanism for the Acceleration of Ultrarelativistic Particles

Cited by in corpus (10)

• Spinning particles in general relativity: Momentum-velocity relation for the Mathisson-Pirani spin condition
• Gravito-electromagnetic analogies
• Center of mass, spin supplementary conditions, and the momentum of spinning particles
• Deviation and precession effects in the field of a weak gravitational wave
• Strains and axial outflows in the field of a rotating black hole
• Cylindrical gravitational waves: C-energy, super-energy and associated dynamical effects
• Observer-dependent tidal indicators in the Kerr spacetime
• Slicing black hole spacetimes
• Repulsive effect for the unbound high energy particles along the rotation axis in the Kerr-Taub-NUT spacetime
• Strains and Jets in Black Hole Fields