197 research outputs found

### Classical Spinning Branes in Curved Backgrounds

The dynamics of a classical branelike object in a curved background is
derived from the covariant stress-energy conservation of the brane matter. The
world sheet equations and boundary conditions are obtained in the pole-dipole
approximation, where nontrivial brane thickness gives rise to its intrinsic
angular momentum. It is shown that intrinsic angular momentum couples to both,
the background curvature and the brane orbital degrees of freedom. The whole
procedure is manifestly covariant with respect to spacetime diffeomorphisms and
world sheet reparametrizations. In addition, two extra gauge symmetries are
discovered and utilized. The examples of the point particle and the string in 4
spacetime dimensions are analyzed in more detail. A particular attention is
paid to the Nambu-Goto string with massive spinning particles attached to its
ends

### Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: a new gauge-invariant post-Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force

The innermost stable circular orbit (ISCO) delimits the transition from
circular orbits to those that plunge into a black hole. In the test-mass limit,
well-defined ISCO conditions exist for the Kerr and Schwarzschild spacetimes.
In the finite-mass case, there are a large variety of ways to define an ISCO in
a post-Newtonian (PN) context. Here I generalize the gauge-invariant ISCO
condition of Blanchet & Iyer (2003) to the case of spinning (nonprecessing)
binaries. The Blanchet-Iyer ISCO condition has two desirable and unexpected
properties: (1) it exactly reproduces the Schwarzschild ISCO in the test-mass
limit, and (2) it accurately approximates the recently-calculated shift in the
Schwarzschild ISCO frequency due to the conservative-piece of the gravitational
self-force [Barack & Sago (2009)]. The generalization of this ISCO condition to
spinning binaries has the property that it also exactly reproduces the Kerr
ISCO in the test-mass limit (up to the order at which PN spin corrections are
currently known). The shift in the ISCO due to the spin of the test-particle is
also calculated. Remarkably, the gauge-invariant PN ISCO condition exactly
reproduces the ISCO shift predicted by the Papapetrou equations for a
fully-relativistic spinning particle. It is surprising that an analysis of the
stability of the standard PN equations of motion is able (without any form of
"resummation") to accurately describe strong-field effects of the Kerr
spacetime. The ISCO frequency shift due to the conservative self-force in Kerr
is also calculated from this new ISCO condition, as well as from the
effective-one-body Hamiltonian of Barausse & Buonanno (2010). These results
serve as a useful point-of-comparison for future gravitational self-force
calculations in the Kerr spacetime.Comment: 17 pages, 2 figures, 1 table. v2: references added; minor changes to
match published versio

### Action based approach to the dynamics of extended bodies in General Relativity

We present, for the first time, an action principle that gives the equations
of motion of an extended body possessing multipole moments in an external
gravitational field, in the weak field limit. From the action, the
experimentally observable quantum phase shifts in the wavefunction of an
extended object due to the coupling of its multipole moments with the
gravitational field are obtained. Also, since the theory may be quantized using
the action, the present approach is useful in the interface between general
relativity and quantum mechanics.Comment: This essay received an ``honorable mention'' in the 2003 Gravity
Research Foundation essay competitio

### Motion of a Vector Particle in a Curved Spacetime. I. Lagrangian Approach

From the simple Lagrangian the equations of motion for the particle with spin
are derived. The spin is shown to be conserved on the particle world-line. In
the absence of a spin the equation coincides with that of a geodesic. The
equations of motion are valid for massless particles as well, since mass does
not enter the equations explicitely.Comment: 6 pages, uses mpla1.sty, published in MPLA, replaced with corrected
typo

### 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

### 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

### Motion of a Vector Particle in a Curved Spacetime. II First Order Correction to a Geodesic in a Schwarzschild Background

The influence of spin on a photon's motion in a Schwarzschild and FRW
spacetimes is studied. The first order correction to the geodesic motion is
found. It is shown that unlike the world-lines of spinless particles, the
photons world-lines do not lie in a plane.Comment: 14 pages, LaTeX2e, second paper in the series (the first one:
gr-qc/0110067), replaced with typos and style corrected version, accepted in
MPL

### Mathisson's helical motions for a spinning particle --- are they unphysical?

It has been asserted in the literature that Mathisson's helical motions are
unphysical, with the argument that their radius can be arbitrarily large. We
revisit Mathisson's helical motions of a free spinning particle, and observe
that such statement is unfounded. Their radius is finite and confined to the
disk of centroids. We argue that the helical motions are perfectly valid and
physically equivalent descriptions of the motion of a spinning body, the
difference between them being the choice of the representative point of the
particle, thus a gauge choice. We discuss the kinematical explanation of these
motions, and we dynamically interpret them through the concept of hidden
momentum. We also show that, contrary to previous claims, the frequency of the
helical motions coincides, even in the relativistic limit, with the
zitterbewegung frequency of the Dirac equation for the electron

### Symmetric Teleparallel Gravity: Some exact solutions and spinor couplings

In this paper we elaborate on the symmetric teleparallel gravity (STPG)
written in a non-Riemannian spacetime with nonzero nonmetricity, but zero
torsion and zero curvature. Firstly we give a prescription for obtaining the
nonmetricity from the metric in a peculiar gauge. Then we state that under a
novel prescription of parallel transportation of a tangent vector in this
non-Riemannian geometry the autoparallel curves coincides with those of the
Riemannian spacetimes. Subsequently we represent the symmetric teleparallel
theory of gravity by the most general quadratic and parity conserving
lagrangian with lagrange multipliers for vanishing torsion and curvature. We
show that our lagrangian is equivalent to the Einstein-Hilbert lagrangian for
certain values of coupling coefficients. Thus we arrive at calculating the
field equations via independent variations. Then we obtain in turn conformal,
spherically symmetric static, cosmological and pp-wave solutions exactly.
Finally we discuss a minimal coupling of a spin-1/2 field to STPG.Comment: Accepted for publication in the International Journal of Modern
Physics

### Dirac equations in curved space-time versus Papapetrou spinning particles

We find out classical particles, starting from Dirac quantum fields on a
curved space-time, by an eikonal approximation and a localization hypothesis
for amplitudes. We recover the results by Mathisson-Papapetrou, hence
establishing a fundamental correspondence between the coupling of classical and
quantum spinning particles with the gravitational field.Comment: 6 pages, 1 figure, accepted for publication in Europhysics Letter

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