231 research outputs found
Fermat Principle in Finsler Spacetimes
It is shown that, on a manifold with a Finsler metric of Lorentzian
signature, the lightlike geodesics satisfy the following variational principle.
Among all lightlike curves from a point (emission event) to a timelike curve
(worldline of receiver), the lightlike geodesics make the arrival time
stationary. Here ``arrival time'' refers to a parametrization of the timelike
curve. This variational principle can be applied (i) to the vacuum light rays
in an alternative spacetime theory, based on Finsler geometry, and (ii) to
light rays in an anisotropic non-dispersive medium with a general-relativistic
spacetime as background.Comment: 18 pages, submitted to Gen. Rel. Gra
A comparison of approximate gravitational lens equations and a proposal for an improved new one
Keeping the exact general relativistic treatment of light bending as a
reference, we compare the accuracy of commonly used approximate lens equations.
We conclude that the best approximate lens equation is the Ohanian lens
equation, for which we present a new expression in terms of distances between
observer, lens and source planes. We also examine a realistic gravitational
lensing case, showing that the precision of the Ohanian lens equation might be
required for a reliable treatment of gravitational lensing and a correct
extraction of the full information about gravitational physics.Comment: 11 pages, 6 figures, to appear on Physical Review
Study of errors in strong gravitational lensing
We examine the accuracy of strong gravitational lensing determinations of the
mass of galaxy clusters by comparing the conventional approach with the
numerical integration of the fully relativistic null geodesic equations in the
case of weak gravitational perturbations on Robertson-Walker metrics. In
particular, we study spherically-symmetric, three-dimensional singular
isothermal sphere models and the three-dimensional matter distribution of
Navarro et al. (1997), which are both commonly used in gravitational lensing
studies. In both cases we study two different methods for mass-density
truncation along the line of sight: hard truncation and conventional (no
truncation). We find that the relative error introduced in the total mass by
the thin lens approximation alone is less than 0.3% in the singular isothermal
sphere model, and less than 2% in the model of Navarro et al. (1997). The
removal of hard truncation introduces an additional error of the same order of
magnitude in the best case, and up to an order of magnitude larger in the worst
case studied. Our results ensure that the future generation of precision
cosmology experiments based on lensing studies will not require the removal of
the thin-lens assumption, but they may require a careful handling of
truncation.Comment: accepted to Ap
Kerr black hole lensing for generic observers in the strong deflection limit
We generalize our previous work on gravitational lensing by a Kerr black hole
in the strong deflection limit, removing the restriction to observers on the
equatorial plane. Starting from the Schwarzschild solution and adding
corrections up to the second order in the black hole spin, we perform a
complete analytical study of the lens equation for relativistic images created
by photons passing very close to a Kerr black hole. We find out that, to the
lowest order, all observables (including shape and shift of the black hole
shadow, caustic drift and size, images position and magnification) depend on
the projection of the spin on a plane orthogonal to the line of sight. In order
to break the degeneracy between the black hole spin and its inclination
relative to the observer, it is necessary to push the expansion to higher
orders. In terms of future VLBI observations, this implies that very accurate
measures are needed to determine these two parameters separately.Comment: 17 pages, 4 figures, one section added, to appear on Physical Review
Wave propagation in axion electrodynamics
In this paper, the axion contribution to the electromagnetic wave propagation
is studied. First we show how the axion electrodynamics model can be embedded
into a premetric formalism of Maxwell electrodynamics. In this formalism, the
axion field is not an arbitrary added Chern-Simon term of the Lagrangian, but
emerges in a natural way as an irreducible part of a general constitutive
tensor.We show that in order to represent the axion contribution to the wave
propagation it is necessary to go beyond the geometric approximation, which is
usually used in the premetric formalism. We derive a covariant dispersion
relation for the axion modified electrodynamics. The wave propagation in this
model is studied for an axion field with timelike, spacelike and null
derivative covectors. The birefringence effect emerges in all these classes as
a signal of Lorentz violation. This effect is however completely different from
the ordinary birefringence appearing in classical optics and in premetric
electrodynamics. The axion field does not simple double the ordinary light cone
structure. In fact, it modifies the global topological structure of light cones
surfaces. In CFJ-electrodynamics, such a modification results in violation of
causality. In addition, the optical metrics in axion electrodynamics are not
pseudo-Riemannian. In fact, for all types of the axion field, they are even
non-Finslerian
On Fermat's principle for causal curves in time oriented Finsler spacetimes
In this work, a version of Fermat's principle for causal curves with the same
energy in time orientable Finsler spacetimes is proved. We calculate the
secondvariation of the {\it time arrival functional} along a geodesic in terms
of the index form associated with the Finsler spacetime Lagrangian. Then the
character of the critical points of the time arrival functional is investigated
and a Morse index theorem in the context of Finsler spacetime is presented.Comment: 20 pages, minor corrections, references adde
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
Possible potentials responsible for stable circular relativistic orbits
Bertrand's theorem in classical mechanics of the central force fields
attracts us because of its predictive power. It categorically proves that there
can only be two types of forces which can produce stable, circular orbits. In
the present article an attempt has been made to generalize Bertrand's theorem
to the central force problem of relativistic systems. The stability criterion
for potentials which can produce stable, circular orbits in the relativistic
central force problem has been deduced and a general solution of it is
presented in the article. It is seen that the inverse square law passes the
relativistic test but the kind of force required for simple harmonic motion
does not. Special relativistic effects do not allow stable, circular orbits in
presence of a force which is proportional to the negative of the displacement
of the particle from the potential center.Comment: 11 pages, Latex fil
Vector and Tensor Contributions to the Luminosity Distance
We compute the vector and tensor contributions to the luminosity distance
fluctuations in first order perturbation theory and we expand them in spherical
harmonics. This work presents the formalism with a first application to a
stochastic background of primordial gravitational waves.Comment: 14 pages, 3 figure
- …