Related papers: Deriving Mathisson - Papapetrou equations from rel…
This paper formulates, via the Mathisson - Papapetrou - Dixon equations, the system of equations for a test particle with spin when it is orbiting a weak Kerr metric. We shall restrict ourselves to the case of circular orbits with the…
The Hamiltonian formulation of the motion of a spinning relativistic particle in an external electromagnetic field is considered. The approach is based on the introduction of new coordinates and their conjugated momenta to describe the spin…
It is well known that the equations of motion obtained from Newtons second law of motion can be obtained from a Lagrangian via the Euler-Lagrangian formulation if and only if the equations of motion satisfy the Helmholtz conditions. In this…
In this letter, we discuss the extension of Feynman's derivation of the equation of motion to the case of spinning particles. We show that a spinning particle interacts only with the electromagnetic and gravitational fields. In the absence…
We generalize the $f(R)$ type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$ and of the matter Lagrangian $L_m$. We obtain the gravitational field equations in the…
In our previous article [4] an approach to derive Papapetrou equations for constrained electromagnetic field was demonstrated by use of field variational principles. The aim of current work is to present more universal technique of…
Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations in the Lagrangian formulation correspond to the minimal interaction of spin with gravity. Due to the interaction, in the Lagrangian equations instead of the original metric $g$ emerges…
The interaction between spin and gravitational waves causes spinning bodies to deviate from their geodesics. In this work, we obtain the analytic solution of the Mathisson--Papapetrou--Dixon equations at linear order in the spin for plane…
We discuss the motion of extended objects in a spacetime by considering a gravitational field created by these objects. We define multipole moments of the objects as a classification by Lie group SO(3). Then, we construct an energy-momentum…
We consider the motion of spinning test particles with nonzero rest mass in the "pole-dipole" approximation, as described by the Mathisson-Papapetrou-Dixon (MPD) equations, and examine its properties in dependence on the spin supplementary…
We construct the action of a non-relativistic spinning particle moving in a general torsionless Newton-Cartan background. The particle does not follow the geodesic equations, instead the motion is governed by the non-relativistic analog of…
We construct the Lagrangian formulation of a micro-structured spinning, dilating and shearing (deformable) test body, moving in arbitrary non-Riemannian backgrounds possessing all geometrical entities of curvature, torsion and…
The Euler-Lagrange equations of motion for the most general Ricci type gravitational Lagrangians are derived by means of a purely metric formalism.
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. A simple derivation of the spin interaction with gravitational field is presented. The self-consistent description of the spin…
We present a derivation of the equation of motion for a test-particle in the framework of the nonsymmetric gravitational theory. Three possible couplings of the test-particle to the non-symmetric gravitational field are explored. The…
In continuum physics is presupposed that general-relativistic balance equations are valid which are created from the Lorentz-covariant ones by application of the equivalence principle. Consequently, the question arises, how to make these…
We consider variation of energy of the light-like particle in the pseudo-Riemann space-time, find Lagrangian, canonical momenta and forces. Equations of the critical curve are obtained by the nonzero energy integral variation in accordance…
The Mathisson-Papapetrou-Dixon (MPD) equations, providing the "pole-dipole" description of spinning test particles in general relativity, have to be supplemented by a condition specifying the worldline that will represent the history of the…
Applying Dixon's general equations of motion for extended bodies, we compute the Papapetrou's equations for an extended test body on static and isotropic metrics. We incorporate the force and the torque terms which involve multipole…
Equations of spinning objects are obtained in Absolute Parallelism Geometry [AP], a special class of non-Riemannian geometry admitting an alternative non-vanishing curvature and torsion simultaneously. This new set of equations is the…