352 research outputs found
Strong lensing by fermionic dark matter in galaxies
It has been shown that a self-gravitating system of massive keV fermions in
thermodynamic equilibrium correctly describes the dark matter (DM) distribution
in galactic halos and predicts a denser quantum core towards the center of the
configuration. Such a quantum core, for a fermion mass in the range of keV
keV, can be an alternative interpretation of the
central compact object in Sgr A*. We present in this work the gravitational
lensing properties of this novel DM model in Milky Way-like spiral galaxies. We
describe the lensing effects of the pure DM component both on halo scales,
where we compare them to the effects of the Navarro-Frenk-White and the
Non-Singular Isothermal Sphere DM models, and near the galaxy center, where we
compare them with the effects of a Schwarzschild BH. For the particle mass
leading to the most compact DM core, keV, we draw the
following conclusions. At distances pc from the center of the
lens the effect of the central object on the lensing properties is negligible.
However, we show that measurements of the deflection angle produced by the DM
distribution in the outer region at a few kpc, together with rotation curve
data, could help to discriminate between different DM models. We show that at
distances pc strong lensing effects, such as multiple images and
Einstein rings, may occur. Large differences in the deflection angle produced
by a DM central core and a central BH appear at distances
pc; in this regime the weak-field formalism is no longer applicable and the
exact general-relativistic formula has to be used. We find that quantum DM
cores do not show a photon sphere what implies that they do not cast a shadow.
Similar conclusions apply to the other DM distributions for other fermion
masses in the above specified range and for other galaxy types.Comment: 10 pages, 8 figures. v2: Version published in PR
Gravitational lensing in spherically symmetric static spacetimes with centrifugal force reversal
In Schwarzschild spacetime the value of the radius coordinate is
characterized by three different properties: (a) there is a ``light sphere'',
(b) there is ``centrifugal force reversal'', (c) it is the upper limiting
radius for a non-transparent Schwarschild source to act as a gravitational lens
that produces infinitely many images. In this paper we prove a theorem to the
effect that these three properties are intimately related in {\em any}
spherically symmetric static spacetime. We illustrate the general results with
some examples including black-hole spacetimes and Morris-Thorne wormholes.Comment: 18 pages, 3 eps-figure
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
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
A Morse-theoretical analysis of gravitational lensing by a Kerr-Newman black hole
Consider, in the domain of outer communication of a Kerr-Newman black hole, a
point (observation event) and a timelike curve (worldline of light source).
Assume that the worldline of the source (i) has no past end-point, (ii) does
not intersect the caustic of the past light-cone of the observation event, and
(iii) goes neither to the horizon nor to infinity in the past. We prove that
then for infinitely many positive integers k there is a past-pointing lightlike
geodesic of (Morse) index k from the observation event to the worldline of the
source, hence an observer at the observation event sees infinitely many images
of the source. Moreover, we demonstrate that all lightlike geodesics from an
event to a timelike curve in the domain of outer communication are confined to
a certain spherical shell. Our characterization of this spherical shell shows
that in the Kerr-Newman spacetime the occurrence of infinitely many images is
intimately related to the occurrence of centrifugal-plus-Coriolis force
reversal.Comment: 14 pages, 2 figures; REVTEX; submitted to J. Math. Phy
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
On the energy functional on Finsler manifolds and applications to stationary spacetimes
In this paper we first study some global properties of the energy functional
on a non-reversible Finsler manifold. In particular we present a fully detailed
proof of the Palais--Smale condition under the completeness of the Finsler
metric. Moreover we define a Finsler metric of Randers type, which we call
Fermat metric, associated to a conformally standard stationary spacetime. We
shall study the influence of the Fermat metric on the causal properties of the
spacetime, mainly the global hyperbolicity. Moreover we study the relations
between the energy functional of the Fermat metric and the Fermat principle for
the light rays in the spacetime. This allows us to obtain existence and
multiplicity results for light rays, using the Finsler theory. Finally the case
of timelike geodesics with fixed energy is considered.Comment: 23 pages, AMSLaTeX. v4 matches the published versio
New superintegrable models with position-dependent mass from Bertrand's Theorem on curved spaces
A generalized version of Bertrand's theorem on spherically symmetric curved
spaces is presented. This result is based on the classification of
(3+1)-dimensional (Lorentzian) Bertrand spacetimes, that gives rise to two
families of Hamiltonian systems defined on certain 3-dimensional (Riemannian)
spaces. These two systems are shown to be either the Kepler or the oscillator
potentials on the corresponding Bertrand spaces, and both of them are maximally
superintegrable. Afterwards, the relationship between such Bertrand
Hamiltonians and position-dependent mass systems is explicitly established.
These results are illustrated through the example of a superintegrable
(nonlinear) oscillator on a Bertrand-Darboux space, whose quantization and
physical features are also briefly addressed.Comment: 13 pages; based in the contribution to the 28th International
Colloquium on Group Theoretical Methods in Physics, Northumbria University
(U.K.), 26-30th July 201
On the exact gravitational lens equation in spherically symmetric and static spacetimes
Lensing in a spherically symmetric and static spacetime is considered, based
on the lightlike geodesic equation without approximations. After fixing two
radius values r_O and r_S, lensing for an observation event somewhere at r_O
and static light sources distributed at r_S is coded in a lens equation that is
explicitly given in terms of integrals over the metric coefficients. The lens
equation relates two angle variables and can be easily plotted if the metric
coefficients have been specified; this allows to visualize in a convenient way
all relevant lensing properties, giving image positions, apparent brightnesses,
image distortions, etc. Two examples are treated: Lensing by a
Barriola-Vilenkin monopole and lensing by an Ellis wormhole.Comment: REVTEX, 11 pages, 12 eps-figures, figures partly improved, minor
revision
Strong lensing by fermionic dark matter in galaxies
It has been shown that a self-gravitating system of massive keV fermions in thermodynamic equilibrium correctly describes the dark matter (DM) distribution in galactic halos (from dwarf to spiral and elliptical galaxies) and that, at the same time, it predicts a denser quantum core towards the center of the configuration. Such a quantum core, for a fermion mass in the range of 50 keV ≲m c2≲345 keV , can be an alternative interpretation of the central compact object in Sgr A*, traditionally assumed to be a black hole (BH). We present in this work the gravitational lensing properties of this novel DM configuration in nearby Milky-Way-like spiral galaxies. We describe the lensing effects of the pure DM component both on halo scales, where we compare them to the effects of the Navarro-Frenk-White and the nonsingular isothermal sphere DM models, and near the galaxy center, where we compare them with the effects of a Schwarzschild BH. For the particle mass leading to the most compact DM core, m c2≈1 02 keV , we draw the following conclusions. At distances r ≳20 pc from the center of the lens the effect of the central object on the lensing properties is negligible. However, we show that measurements of the deflection angle produced by the DM distribution in the outer region at a few kpc, together with rotation curve data, could help to discriminate between different DM models. In the inner regions 1 0-6≲r ≲20 pc , the lensing effects of a DM quantum core alternative to the BH scenario becomes a theme of an analysis of unprecedented precision which is challenging for current technological developments. We show that at distances ?1 0-4 pc strong lensing effects, such as multiple images and Einstein rings, may occur. Large differences in the deflection angle produced by a DM central core and a central BH appear at distances r ≲1 0-6 pc ; in this regime the weak-field formalism is no longer applicable and the exact general-relativistic formula has to be used for the deflection angle which may become bigger than 2 π . An important difference in comparison to BHs is in the fact that quantum DM cores do not show a photon sphere; this implies that they do not cast a shadow (if they are transparent). Similar conclusions apply to the other DM distributions for other fermion masses in the above-specified range and for other galaxy types.Facultad de Ciencias Astronómicas y Geofísica
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