On a gravitational analogue of the Aharonov–Bohm effect (original) (raw)
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On a generalized gravitational Aharonov-Bohm effect
2003
A massless spinor particle is considered in the background gravitational field due to a rotating body. In the weak field approximation it is shown that the solution of the Weyl equations depend on the angular momentum of the rotating body, which does not affect the curvature in this approximation. This result may be looked upon as a generalization of the gravitational Aharonov-Bohm effect.
Spin dynamics in gravitational fields of rotating bodies and the equivalence principle
Physical Review D, 2009
We discuss the quantum and classical dynamics of a particle with spin in the gravitational field of a rotating source. A relativistic equation describing the motion of classical spin in curved spacetimes is obtained. We demonstrate that the precession of the classical spin is in a perfect agreement with the motion of the quantum spin derived from the Foldy-Wouthuysen approach for the Dirac particle in a curved spacetime. We show that the precession effect depends crucially on the choice of a tetrad. The results obtained are compared to the earlier computations for different tetrad gauges.
Some Remarks on the Gravitational Aharonov–Bohm Effect
Modern Physics Letters A, 2004
A massless spinor particle is considered in the background spacetimes generated by a moving mass current and by a spinning cosmic string. In the weak field approximation it is shown that the solution of the Weyl equations depends on the velocity of the source, which does not affect the curvature in this approximation in the case of a moving mass current. In the case of a spinning cosmic string, the solution of the Weyl equations depends on the deficit angle and on the angular momentum of the string. These effects may be viewed as examples of the gravitational analogues of the Aharonov–Bohm effect in electrodynamics.
Gravitomagnetism and spinor quantum mechanics
Physical Review D, 2012
We give a systematic treatment of a spin 1/2 particle in a combined electromagnetic field and a weak gravitational field that is produced by a slowly moving matter source. This paper continues previous work on a spin zero particle, but it is largely self-contained and may serve as an introduction to spinors in a Riemann space. The analysis is based on the Dirac equation expressed in generally covariant form and coupled minimally to the electromagnetic field. The restriction to a slowly moving matter source, such as the earth, allows us to describe the gravitational field by a gravitoelectric (Newtonian) potential and a gravitomagnetic (frame-dragging) vector potential, the existence of which has recently been experimentally verified. Our main interest is the coupling of the orbital and spin angular momenta of the particle to the gravitomagnetic field. Specifically we calculate the gravitational gyromagnetic ratio as g g = 1 ; this is to be compared with the electromagnetic gyromagnetic ratio of g e = 2 for a Dirac electron.
Spin in an arbitrary gravitational field
Physical Review D, 2013
We study the quantum mechanics of a Dirac fermion on a curved spacetime manifold. The metric of the spacetime is completely arbitrary, allowing for the discussion of all possible inertial and gravitational field configurations. In this framework, we find the Hermitian Dirac Hamiltonian for an arbitrary classical external field (including the gravitational and electromagnetic ones). In order to discuss the physical content of the quantum-mechanical model, we further apply the Foldy-Wouthuysen transformation, and derive the quantum equations of motion for the spin and position operators. We analyse the semiclassical limit of these equations and compare the results with the dynamics of a classical particle with spin in the framework of the standard Mathisson-Papapetrou theory and in the classical canonical theory. The comparison of the quantum mechanical and classical equations of motion of a spinning particle in an arbitrary gravitational field shows their complete agreement.
arXiv High Energy Astrophysical Phenomena, 2019
The Mathisson-Papapetrou equations are used for investigations of influence of the spin-gravity coupling on a highly relativistic spinning particle in Schwarzschild's field. It is established that interaction of the particle spin with the gravitomagnetic components of the field, estimated in the proper frame of the particle, causes the large acceleration of the spinning particle relative to geodesic free fall. As a result the accelerated charged spinning particle can generate intensive electromagnetic radiation when its velocity is highly relativistic. The significant contribution of the highly relativistic spin-gravity coupling to the energy of the spinning particle is analyzed.
On Reaction of a Spinning Particle on the Spacetime Curvature
Ukrainian Journal of Physics, 2019
The reaction of a classical (nonquantum) spinning particle on the spacetime curvature according to the Mathisson–Papapetrou equations is analyzed. From the point of view of the observer comoving with the particle in Schwarzschild’s field, this reaction is a reaction on the gravitomagnetic components of the gravitational field. The values of these components significantly depend on the relativistic Lorentz factor calculated by the particle velocity relative to the Schwarzschild mass. As a result, the value of the spinning particle acceleration relative to the geodesic motion is proportional to the second power of the Lorentz factor. At the same time, the intensity of the electromagnetic radiation of a charged spinning particle is proportional to the fourth power of this factor. Some numerical estimates are presented.
Classical spinning particles interacting with external gravitational fields
Nuclear Physics B, 1977
In this paper we study the coupling between the pseudoclassical spinning particle and an arbitrary gravitational field. The gravitational field is treated as a gauge field in order to deal with possible contributions from the torsion of space-time. We find that the spinning particle cannot be coupled directly to the torsion. We study the classical equations of motion which turn out to be the same as derived by Papapetrou in order to describe the so called pole-dipole singularity in general relativity. We discuss also the structure of the energy-momentum tensor for the spinning particle.
Rotation Effects and The Gravito‐Magnetic Approach
AIP Conference Proceedings, 2005
Gravito-electromagnetism is somewhat ubiquitous in relativity. In fact, there are many situations where the effects of gravitation can be described by formally introducing "gravito-electric" and "gravito-magnetic" fields, starting from the corresponding potentials, in analogy with the electromagnetic theory[1],[2] (see also A. Tartaglia's contribution to these proceedings). The "many faces of gravito-electromagnetism"[3] are related to rotation effects in both approximated and full theory approaches. Here we show that, by using a 1+3 splitting, relativistic dynamics can be described in terms of gravito-electromagnetic (GEM) fields in full theory. On the basis of this formalism, we introduce a "gravito-magnetic Aharonov-Bohm effect", which allows to interpret some rotation effects as gravito-magnetic effects. Finally, we suggest a way for measuring the angular momentum of celestial bodies by studying the gravito-magnetic effects on the propagation of electromagnetic signals.
A spinning particle in a gravitational field
Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki, 1989
The equations of motion of a spinning particle in an external gravitational field are derived. The additional force making the motion nongeodesic is a gravitational analog of the Lorentz force. Considerations which define the general form of the wave equation for particles with arbitrary spin in electromagnetic and gravitational fields are presented.