80 research outputs found
Motion of test bodies in theories with nonminimal coupling
We derive the equations of motion of test bodies for a theory with nonminimal
coupling by means of a multipole method. The propagation equations for
pole-dipole particles are worked out for a gravity theory with a very general
coupling between the curvature scalar and the matter fields. Our results allow
for a systematic comparison with the equations of motion of general relativity
and other gravity theories.Comment: 5 pages, RevTex forma
The de Sitter Relativistic Top Theory
We discuss the relativistic top theory from the point of view of the de
Sitter (or anti de Sitter) group. Our treatment rests on Hanson-Regge's
spherical relativistic top lagrangian formulation. We propose an alternative
method for studying spinning objects via Kaluza-Klein theory. In particular, we
derive the relativistic top equations of motion starting with the geodesic
equation for a point particle in 4+N dimensions. We compare our approach with
the Fukuyama's formulation of spinning objects, which is also based on
Kaluza-Klein theory. We also report a generalization of our approach to a 4+N+D
dimensional theory.Comment: 25 pages, Latex,commnets and references adde
Dynamics of test bodies with spin in de Sitter spacetime
We study the motion of spinning test bodies in the de Sitter spacetime of
constant positive curvature. With the help of the 10 Killing vectors, we derive
the 4-momentum and the tensor of spin explicitly in terms of the spacetime
coordinates. However, in order to find the actual trajectories, one needs to
impose the so-called supplementary condition. We discuss the dynamics of
spinning test bodies for the cases of the Frenkel and Tulczyjew conditions.Comment: 11 pages, RevTex forma
Spinning branes in Riemann-Cartan spacetime
We use the conservation law of the stress-energy and spin tensors to study
the motion of massive brane-like objects in Riemann-Cartan geometry. The
world-sheet equations and boundary conditions are obtained in a manifestly
covariant form. In the particle case, the resultant world-line equations turn
out to exhibit a novel spin-curvature coupling. In particular, the spin of a
zero-size particle does not couple to the background curvature. In the string
case, the world-sheet dynamics is studied for some special choices of spin and
torsion. As a result, the known coupling to the Kalb-Ramond antisymmetric
external field is obtained. Geometrically, the Kalb-Ramond field has been
recognized as a part of the torsion itself, rather than the torsion potential
The Schroedinger operator as a generalized Laplacian
The Schroedinger operators on the Newtonian space-time are defined in a way
which make them independent on the class of inertial observers. In this picture
the Schroedinger operators act not on functions on the space-time but on
sections of certain one-dimensional complex vector bundle -- the Schroedinger
line bundle. This line bundle has trivializations indexed by inertial observers
and is associated with an U(1)-principal bundle with an analogous list of
trivializations -- the Schroedinger principal bundle. For the Schroedinger
principal bundle a natural differential calculus for `wave forms' is developed
that leads to a natural generalization of the concept of Laplace-Beltrami
operator associated with a pseudo-Riemannian metric. The free Schroedinger
operator turns out to be the Laplace-Beltrami operator associated with a
naturally distinguished invariant pseudo-Riemannian metric on the Schroedinger
principal bundle. The presented framework is proven to be strictly related to
the frame-independent formulation of analytical Newtonian mechanics and
Hamilton-Jacobi equations, that makes a bridge between the classical and
quantum theory.Comment: 19 pages, a remark, an example and references added - the version to
appear in J. Phys. A: Math. and Theo
Highly relativistic spinning particle starting near in a Kerr field
Using the Mathisson-Papapetrou-Dixon (MPD) equations, we investigate the
trajectories of a spinning particle starting near in a Kerr
field and moving with the velocity close to the velocity of light
( is the Boyer-Lindquist radial coordinate of the
counter-rotation circular photon orbits). First, as a partial case of these
trajectories, we consider the equatorial circular orbit with .
This orbit is described by the solution that is common for the rigorous MPD
equations and their linear spin approximation. Then different cases of the
nonequatorial motions are computed and illustrated by the typical figures. All
these orbits exhibit the effects of the significant gravitational repulsion
that are caused by the spin-gravity interaction. Possible applications in
astrophysics are discussed.Comment: 10 pages, 12 figure
Classical String in Curved Backgrounds
The Mathisson-Papapetrou method is originally used for derivation of the
particle world line equation from the covariant conservation of its
stress-energy tensor. We generalize this method to extended objects, such as a
string. Without specifying the type of matter the string is made of, we obtain
both the equations of motion and boundary conditions of the string. The world
sheet equations turn out to be more general than the familiar minimal surface
equations. In particular, they depend on the internal structure of the string.
The relevant cases are classified by examining canonical forms of the effective
2-dimensional stress-energy tensor. The case of homogeneously distributed
matter with the tension that equals its mass density is shown to define the
familiar Nambu-Goto dynamics. The other three cases include physically relevant
massive and massless strings, and unphysical tahyonic strings.Comment: 12 pages, REVTeX 4. Added a note and one referenc
Scattering of Spinning Test Particles by Plane Gravitational and Electromagnetic Waves
The Mathisson-Papapetrou-Dixon (MPD) equations for the motion of electrically
neutral massive spinning particles are analysed, in the pole-dipole
approximation, in an Einstein-Maxwell plane-wave background spacetime. By
exploiting the high symmetry of such spacetimes these equations are reduced to
a system of tractable ordinary differential equations. Classes of exact
solutions are given, corresponding to particular initial conditions for the
directions of the particle spin relative to the direction of the propagating
background fields. For Einstein-Maxwell pulses a scattering cross section is
defined that reduces in certain limits to those associated with the scattering
of scalar and Dirac particles based on classical and quantum field theoretic
techniques. The relative simplicity of the MPD approach and its use of
macroscopic spin distributions suggests that it may have advantages in those
astrophysical situations that involve strong classical gravitational and
electromagnetic environments.Comment: Submitted to Classical and Quantum Gravity. 12 page
On the motion of spinning test particles in plane gravitational waves
The Mathisson-Papapetrou-Dixon equations for a massive spinning test particle
in plane gravitational waves are analysed and explicit solutions constructed in
terms of solutions of certain linear ordinary differential equations. For
harmonic waves this system reduces to a single equation of Mathieu-Hill type.
In this case spinning particles may exhibit parametric excitation by
gravitational fields. For a spinning test particle scattered by a gravitational
wave pulse, the final energy-momentum of the particle may be related to the
width, height, polarisation of the wave and spin orientation of the particle.Comment: 11 page
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