Nonlocal Gravitomagnetism

We briefly review the current status of nonlocal gravity (NLG), which is a classical nonlocalgeneralization of Einstein’s theory of gravitation based on a certain analogy with the nonlocalelectrodynamics of media. Nonlocal gravity thus involves integro-differential field equationsand a causal constitutive kernel that should ultimately be determined from observational data.We consider the stationary gravitational field of an isolated rotating astronomical source in the linearapproximation of nonlocal gravity. In this weak-field and slow-motion approximation of NLG,we describe the gravitomagnetic field associated with the rotating source and compare our resultswith gravitoelectromagnetism (GEM) of the standard general relativity theory. Moreover, we brieflystudy the energy-momentum content of the GEM field in nonlocal gravity.

ELECTROMAGNETIC EFFECTS IN SUPERCONDUCTORS IN STATIONARY GRAVITATIONAL FIELD

The general relativistic modifications to the resistive state in superconductors of second type in the presence of a stationary gravitational field are studied. Some superconducting devices that can measure the gravitational field by its red-shift effect on the frequency of radiation are suggested. It has been shown that by varying the orientation of a superconductor with respect to the earth gravitational field, a corresponding varying contribution to AC Josephson frequency would be added by gravity. A magnetic flux (being proportional to angular velocity of rotation Ω) through a rotating hollow superconducting cylinder with the radial gradient of temperature ∇rT is theoretically predicted. The magnetic flux is assumed to be produced by the azimuthal current arising from Coriolis force effect on radial thermoelectric current. Finally the magnetic flux through the superconducting ring with radial heat flow located at the equatorial plane interior of the rotating neutron star is calculated. In particular it has been shown that nonvanishing magnetic flux will be generated due to the general relativistic effect of dragging of inertial frames on the thermoelectric current.

QUASI-STATIONARY ELECTROMAGNETIC EFFECTS IN CONDUCTORS AND SUPERCONDUCTORS IN SCHWARZSCHILD SPACE–TIME

The general principles needed to compute the effect of a stationary gravitational field on the quasistationary electromagnetic phenomena in normal conductors and superconductors are formulated from general relativistic point of view. Generalization of the skin effect, that is the general relativistic modification of the penetration depth (of the time-dependent magnetic field in the conductor) due to its relativistic coupling to the gravitational field is obtained. The effect of the gravitational field on the penetration and coherence depths in superconductors is also studied. As an illustration of the foregoing general results, we discuss their application to superconducting systems in the outer core of neutron stars. The relevance of these effects to electrodynamics of magnetized neutron stars has been shown.

Relativistic Reduction of Astrometric Observations at Points Level of Accuracy

The framework of general relativity theory (GRT) is applied to the problem of reduction of high precision astrometric observations of the order of one microarcsecond. The equations of geometric optics for the non-stationary gravitational field of the Solar system have been deduced. Integration of the equations of geometric optics results in the isotropic geodesic line connecting the source of emission (a star, a quasar) and an observer. This permits to calculate the effects of relativistic aberration of light due to monopole and quadrupole components of the gravitational field of the Sun and the planets taking into account their motions and rotation. Transformations between the reference systems are used to calculate the light aberration occurring when passing from the satellite system to the geocentric system and from the geocentric system to the baryecntric system. The baryecntric components of the observed position vector reduced to the flat space-time are corrected, if necessary, for parallax and proper motion of a celestial object using the classical techniques of Euclidean geometry.