4,408 research outputs found
Spin Hall effect of Photons in a Static Gravitational Field
Starting from a Hamiltonian description of the photon within the set of
Bargmann-Wigner equations we derive new semiclassical equations of motion for
the photon propagating in static gravitational field. These equations which are
obtained in the representation diagonalizing the Hamiltonian at the order
, present the first order corrections to the geometrical optics. The
photon Hamiltonian shows a new kind of helicity-magnetotorsion coupling.
However, even for a torsionless space-time, photons do not follow the usual
null geodesic as a consequence of an anomalous velocity term. This term is
responsible for the gravitational birefringence phenomenon: photons with
distinct helicity follow different geodesics in a static gravitational field.Comment: 6 page
A Characterisation of the Weylian Structure of Space-Time by Means of Low Velocity Tests
The compatibility axiom in Ehlers, Pirani and Schild's (EPS) constructive
axiomatics of the space-time geometry that uses light rays and freely falling
particles with high velocity, is replaced by several constructions with low
velocity particles only. For that purpose we describe in a space-time with a
conformal structure and an arbitrary path structure the radial acceleration, a
Coriolis acceleration and the zig-zag construction. Each of these quantities
give effects whose requirement to vanish can be taken as alternative version of
the compatibility axiom of EPS. The procedural advantage lies in the fact, that
one can make null-experiments and that one only needs low velocity particles to
test the compatibility axiom. We show in addition that Perlick's standard clock
can exist in a Weyl space only.Comment: to appear in Gen.Rel.Gra
The Theory of Caustics and Wavefront Singularities with Physical Applications
This is intended as an introduction to and review of the work of V, Arnold
and his collaborators on the theory of Lagrangian and Legendrian submanifolds
and their associated maps. The theory is illustrated by applications to
Hamilton-Jacobi theory and the eikonal equation, with an emphasis on null
surfaces and wavefronts and their associated caustics and singularities.Comment: Figs. not include
On the structure of the post-Newtonian expansion in general relativity
In the continuation of a preceding work, we derive a new expression for the
metric in the near zone of an isolated matter system in post-Newtonian
approximations of general relativity. The post-Newtonian metric, a solution of
the field equations in harmonic coordinates, is formally valid up to any order,
and is cast in the form of a particular solution of the wave equation, plus a
specific homogeneous solution which ensures the asymptotic matching to the
multipolar expansion of the gravitational field in the exterior of the system.
The new form provides some insights on the structure of the post-Newtonian
expansion in general relativity and the gravitational radiation reaction terms
therein.Comment: 22 pages, to appear in Phys. Rev.
Conformal symmetry and deflationary gas universe
We describe the ``deflationary'' evolution from an initial de Sitter phase to
a subsequent Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) period as a
specific non-equilibrium configuration of a self-interacting gas. The
transition dynamics corresponds to a conformal, timelike symmetry of an
``optical'' metric, characterized by a refraction index of the cosmic medium
which continously decreases from a very large initial value to unity in the
FLRW phase.Comment: 10 pages, to appear in "Exact Solutions and Scalar Fields in Gravity:
Recent Developments", ed. by A. Macias, J. Cervantes-Cota, and C.
L\"ammerzahl, Kluwer Academic Publishers 200
The Motion of a Body in Newtonian Theories
A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General
Relativity." Journal of Mathematical Physics 16(1), (1975)] provides the sense
in which the geodesic principle has the status of a theorem in General
Relativity (GR). Here we show that a similar theorem holds in the context of
geometrized Newtonian gravitation (often called Newton-Cartan theory). It
follows that in Newtonian gravitation, as in GR, inertial motion can be derived
from other central principles of the theory.Comment: 12 pages, 1 figure. This is the version that appeared in JMP; it is
only slightly changed from the previous version, to reflect small issue
caught in proo
Initial data sets for the Schwarzschild spacetime
A characterisation of initial data sets for the Schwarzschild spacetime is
provided. This characterisation is obtained by performing a 3+1 decomposition
of a certain invariant characterisation of the Schwarzschild spacetime given in
terms of concomitants of the Weyl tensor. This procedure renders a set of
necessary conditions --which can be written in terms of the electric and
magnetic parts of the Weyl tensor and their concomitants-- for an initial data
set to be a Schwarzschild initial data set. Our approach also provides a
formula for a static Killing initial data set candidate --a KID candidate.
Sufficient conditions for an initial data set to be a Schwarzschild initial
data set are obtained by supplementing the necessary conditions with the
requirement that the initial data set possesses a stationary Killing initial
data set of the form given by our KID candidate. Thus, we obtain an algorithmic
procedure of checking whether a given initial data set is Schwarzschildean or
not.Comment: 16 page
A Note on the Symmetries of the Gravitational Field of a Massless Particle
It is shown that the metric of a massless particle obtained from boosting the
Schwarzschild metric to the velocity of light, has four Killing vectors
corresponding to an E(2)\times \RR symmetry-group. This is in agreement with
the expectations based on flat-space kinematics but is in contrast to previous
statements in the literature \cite{Schueck}. Moreover, it also goes beyond the
general Jordan-Ehlers-Kundt-(JEK)-classification of gravitational pp-waves as
given in \cite{JEK}.Comment: 10pages, amslatex, TUW-94-12 and UWThPh-1994-2
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