Classical Gravitational Interactions and Gravitational Lorentz Force

In quantum gauge theory of gravity, the gravitational field is represented by gravitational gauge field. The field strength of gravitational gauge field has both gravitoelectric component and gravitomagnetic component. In classical level, gauge theory of gravity gives classical Newtonian gravitational interactions in a relativistic form. Besides, it gives gravitational Lorentz force, which is the gravitational force on a moving object in gravitomagnetic field. The direction of gravitational Lorentz force is not the same as that of classical gravitational Newtonian force. Effects of gravitational Lorentz force should be detectable, and these effects can be used to discriminate gravitomagnetic field from ordinary electromagnetic magnetic field.     

Classical Gravitational Interactions and Gravitational Lorentz Force

In quantum gauge theory of gravity, the gravitational field is represented by gravitational gauge field.The field strength of gravitational gauge field has both gravitoelectric component and gravitomagnetic component. In classical level, gauge theory of gravity gives classical Newtonian gravitational interactions in a relativistic form. Besides,it gives gravitational Lorentz force, which is the gravitational force on a moving object in gravitomagnetic field The direction of gravitational Lorentz force is not the same as that of classical gravitational Newtonian force. Effects of gravitational Lorentz force should be detectable, and these effects can be used to discriminate gravitomagnetic field from ordinary electromagnetic magnetic field.     

The dual curvature tensors and dynamics of gravitomagnetic matter

Gravitomagnetic charge that can also be referred to as the dual mass or magnetic mass is the topological charge in gravity theory. A gravitomagnetic monopole at rest can produce a stationary gravitomagnetic field. Due to the topological nature of gravitomagnetic charge, the metric of spacetime where the gravitomagnetic matter is present will be nonanalytic. In this paper both the dual curvature tensors (which can characterize the dynamics of gravitational charge/monopoles) and the antisymmetric gravitational field equation of gravitomagnetic matter are presented. We consider and discuss the mathematical formulation and physical properties of the dual curvature tensors and scalar, antisymmetric source tensors, dual spin connection (including the low‐motion weak‐field approximation), dual vierbein field as well as dual current densities of gravitomagnetic charge. It is shown that the dynamics of gravitomagnetic charge can be founded within the framework of the above dual quantities. In addition, the duality relationship in the dynamical theories between the gravitomagnetic charge (dual mass) and the gravitoelectric charge (mass) is also taken into account in the present paper.     

Comments on “Gravitoelectric-Electric Coupling via Superconductivity“ by Douglas G. Torr and Ning Li

Torr and Li claim to have shown that experimentally detectable gravitomagnetic and gravitoelectric fields can be generated in a superconductor. We review their calculations and show that because of unrealistic assumptions the fields that they calculate are too large by many orders of magnitude.     

Absence of a gravitational analog to the Meissner effect

In the framework of the weak stationary gravitational field and low velocity, we investigate the gravitomagnetic effects on a superconductor. We show that we have no gravitomagnetic shielding, and thus no generalized Meissner gravitational effect in superconductors.     

Gravitational Analogues, Geometric Effects and Gravitomagnetic Charge

This essay discusses some geometric effects associated with gravitomagnetic fields and gravitomagnetic charge as well as the gravity theory of the latter. Gravitomagnetic charge is the duality of gravitoelectric charge (mass) and is therefore also termed the dual mass which represents the topological property of gravitation. The field equation of gravitomagnetic matter is suggested and a static spherically symmetric solution of this equation is offered. A possible explanation of the anomalous acceleration acting on Pioneer spacecrafts are briefly proposed.     

Existence of the gravitomagnetic interaction

The point of view expressed in the literature that gravitomagnetism has not yet been observed or measured is not entirely correct. Observations of gravitational phenomena are reviewed in which the gravitomagnetic interaction—a post-Newtonian gravitational force between moving matter—has participated and which has been measured to 1 part in 1000. Gravitomagnetism is shown to be ubiquitous in gravitational phenomena and is a necessary ingredient in the equations of motion, without which the most basic gravitational dynamical effects (including Newtonian gravity) could not be consistently calculated by different inertial observers.     

On the interaction of mesoscopic quantum systems with gravity

We review the different aspects of the interaction of mesoscopic quantum systems with gravitational fields. We first discuss briefly the foundations of general relativity and quantum mechanics. Then, we consider the non‐relativistic expansions of the Klein‐Gordon and Dirac equations in the post‐Newtonian approximation. After a short overview of classical gravitational waves, we discuss two proposed interaction mechanisms: (i) the use of quantum fluids as generator and/or detector of gravitational waves in the laboratory, and (ii) the inclusion of gravitomagnetic fields in the study of the properties of rotating superconductors. The foundations of the proposed experiments are explained and evaluated.     

Teleparallel Gravitoelectromagnetism: The Role of Boosts in the Schwarzschild Geometry

We study the effects of boosts on the gravitoelectric and gravitomagnetic fields, as described in the Teleparallel Equivalent of General Relativity context, and use the Schwarzschild geometry as a primer example, to reaffirm the definitions of the two fields. To draw a parallel with Electrodynamics, we consider the well-known effect of a boost to an observer moving relative to an electrical point charge at rest. The main conclusion is that in the linear regime, when measured from a reference frame under the effect of a boost towards x, the gravitoelectromagnetic components with algebraic index equal to zero are quite analogous to those of Electromagnetism.     

Spin-Spin Interactions in Gauge Theory of Gravity, Violation of Weak Equivalence Principle and New Classical Test of General Relativity

For a long time, it has been generally believed that spin-spin interactions can only exist in a theory where Lorentz symmetry is gauged, and a theory with spin-spin interactions is not perturbatively renormalizable. But this is not true. By studying the motion of a spinning particle in gravitational field, it is found that there exist spin-spin interactions in gauge theory of gravity. Its mechanism is that a spinning particle will generate gravitomagnetic field in space-time, and this gravitomagnetic field will interact with the spin of another particle, which will cause spin-spin interactions. So, spin-spin interactions are transmitted by gravitational field. The form of spin-spin interactions in post Newtonian approximations is deduced. This result can also be deduced from the Papapetrou equation. This kind of interaction will not affect the renormalizability of the theory. The spin-spin interactions will violate the weak equivalence principle, and the violation effects are detectable. An experiment is proposed to detect the effects of the violation of the weak equivalence principle.     

A new approach to studying local gravitomagnetic effects on a superconductor

In this paper we introduce gravitomagnetic field equations into the investigation of gravitomagnetic effects on a superconductor. We point out that in the absence of an applied magnetic field, an applied gravitomagnetic field will induce twin currents, gravitational and electric supercurrents. The latter will create a magnetic field. The slightly modified Josephson, London, and London-type gravitomagnetic equations are obtained. Some applications of these equations are discussed.     

Gravitoelectric-electric coupling via superconductivity

Recently we demonstrated theoretically that the carriers of quantized angular momentum in superconductors are not the Cooper pairs but the lattice ions, which must execute coherent localized motion consistent with the phenomenon of superconductivity. We demonstrate here that in the presence of an external magnetic field, the free superelectron and bound ion currents largely cancel providing a self-consistent microscopic and macroscopic interpretation of near-zero magnetic permeability inside superconductors. The neutral mass currents, however, do not cancel, because of the monopolar gravitational charge. It is shown that the coherent alignment of lattice ion spins will generate a detectable gravitomagnetic field, and in the presence of a time-dependent applied magnetic vector potential field, a detectable gravitoelectric field.     

Gravitomagnetic Effects

The paper summarizes the most important effects in Einsteinian gravitomagnetic fields related to propagating light rays, moving clocks and atoms, orbiting objects, and precessing spins. Emphasis is put onto the gravitational interaction of spinning objects. The gravitomagnetic field lines of a rotating or spinning object are given in analytic form.     

Massive spin-1 gravity and the gravitational flux quantum

We present a derivation of the mass of the graviton inside a superconductor or other quantum coherent matter, starting from the gravitomagnetic equations and using the breaking of U(1) phase rotational symmetry of particles with a macroscopic wavefunction. We arrive at a simple and complete analytical expression for the graviton mass in terms of fundamental constants, with the mass density of the superconductor the only free parameter entering the ratio of photon-to-graviton mass. We compare predictions of our graviton mass with existing experimental data concerning the Tate-Cooper pair mass anomaly [C.J. de Matos, M. Tajmar, Physica C: Superconductivity 432 (2005) 167; J. Tate, B. Cabrera, S.B. Felch, J.T. Anderson, Phys. Rev. Lett. 62 (1989) 845]. We then go on to show that the gravitomagnetic flux through a superconducting ring is quantised and the resulting gravitationally-induced currents are measurable in the laboratory, allowing experimental access to an effect of quantised gravitational flux. We also show that phase change effects in multiply connected superconductors are due to the sum of gravitomagnetic and magnetic flux penetrating the superconductor. Finally, we speculate on the possible relevance to neutron star core formation.     

Concerning Measurement of Gravitomagnetism in Electromagnetic Systems

Measurement of gravitomagnetic field is of fundamental importance as a test of general relativity. Here we present a new theoretical project for performing such a measurement based on detection of the electric field arising from the interplay between the gravitomagnetic and magnetic fields in the stationary axial-symmetric gravitational field of a slowly rotating massive body. Finally it is shown that precise magnetometers based on superconducting quantum interferometers could not be designed for measurement of the gravitomagnetically induced magnetic field in the cavity of a charged capacitor since they measure the circulation of a vector potential of electromagnetic field, i.e., an invariant quantity including the sum of electric and magnetic fields, and the general-relativistic magnetic part will be totally cancelled by the electric one which is in good agreement with the experimental results.     

Letter: Gravitational Potential in the Palatini Formulation of Modified Gravity

General Relativity has so far passed almost all the ground-based and solar-system experiments. Any reasonable extended gravity models should consistently reduce to it at least in the weak field approximation. In this work we derive the gravitational potential for the Palatini formulation of the modified gravity of the L(R) type which admits a de Sitter vacuum solution. We argue that the Newtonian limit is always obtained in those class of models and the deviations from General Relativity are very small for a slowly moving source.     

General relativity in Newtonian form

It is shown how the use of coordinates where time is measured with clocks moving radially in a spherically symmetric gravitational field leads to general relativistic dynamical expressions that are exactly identical to corresponding expressions in Newtonian theory. The general formalism is developed for the case where the stress-energy tensor is that of a perfect fluid. Expressions like the Newtonian inverse square gravitational law, the Newtonian equation of continuity for fluid flow, Newtonian conservation of energy, etc., follow quite naturally from the fully-fledged exact general relativistic equations. Specific examples involving cosmology and gravitational collapse are given.     

Propagation of transverse electromagnetic waves with gravitational perturbations in an isotropic universe

The combined behavior of gravitational and electromagnetic perturbations in the radiation-dominated plasma of an isotropic universe is considered. It is shown that transverse electromagnetic waves and vector and tensor gravitational perturbations are independent of one another. The propagation of transverse electromagnetic waves during the lepton and radiation-dominated phases is determined. It is shown that the gravitational perturbations help to excite longitudinal electromagnetic fields in the radiation-dominated plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 49–54, December, 1985.     

Non-relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity

Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we can see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger equation, which can explain the gravitational phase effects found in COW experiments.And because of this Newtonian gravitational potential, a quantum particle in the earth's gravitational field may form a gravitationally bound quantized state, which has already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are studied in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, and radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.     

Detection of the gravitomagnetic field using an orbiting superconducting gravity gradiometer: principle and experimental considerations

The angular momentum of the Earth produces gravitomagnetic components of the Riemann curvature tensor, which are of the order of 10⁻¹⁰ of the Newtonian terms arising from the mass of the Earth. Due to the dragging of the local inertial frame by the spinning Earth, there are also secular terms, which grow in time. These fields can be detected in principle by a set of orbiting superconducting gravity gradiometers. The Riemann tensor components for various spacecraft orientations have been computed and the principle of detecting the gravitomagnetic tidal force has been published. In this paper, we review the conclusions of the earlier analyses and discuss the feasibility of the gravity gradiometer experiment.