354 research outputs found
Magnification relations for Kerr lensing and testing Cosmic Censorship
A Kerr black hole with mass parameter m and angular momentum parameter a
acting as a gravitational lens gives rise to two images in the weak field
limit. We study the corresponding magnification relations, namely the signed
and absolute magnification sums and the centroid up to post-Newtonian order. We
show that there are post-Newtonian corrections to the total absolute
magnification and centroid proportional to a/m, which is in contrast to the
spherically symmetric case where such corrections vanish. Hence we also propose
a new set of lensing observables for the two images involving these
corrections, which should allow measuring a/m with gravitational lensing. In
fact, the resolution capabilities needed to observe this for the Galactic black
hole should in principle be accessible to current and near-future
instrumentation. Since a/m >1 indicates a naked singularity, a most interesting
application would be a test of the Cosmic Censorship conjecture. The technique
used to derive the image properties is based on the degeneracy of the Kerr lens
and a suitably displaced Schwarzschild lens at post-Newtonian order. A simple
physical explanation for this degeneracy is also given.Comment: 13 pages, version 2: references added, minor changes. To appear in
Phys. Rev.
Formalism for testing theories of gravity using lensing by compact objects. III: Braneworld gravity
Braneworld gravity is a model that endows physical space with an extra
dimension. In the type II Randall-Sundrum braneworld gravity model, the extra
dimension modifies the spacetime geometry around black holes, and changes
predictions for the formation and survival of primordial black holes. We
develop a comprehensive analytical formalism for far-field black hole lensing
in this model, using invariant quantities to compute all geometric optics
lensing observables. We then make the first analysis of wave optics in
braneworld lensing, working in the semi-classical limit. We show that wave
optics offers the only realistic way to observe braneworld effects in black
hole lensing. We point out that if primordial braneworld black holes exist,
have mass M, and contribute a fraction f of the dark matter, then roughly 3e5 x
f (M/1e-18 Msun)^(-1) of them lie within our Solar System. These objects, which
we call "attolenses," would produce interference fringes in the energy spectra
of gamma-ray bursts at energies ~100 (M/1e-18 Msun)^(-1) MeV (which will soon
be accessible with the GLAST satellite). Primordial braneworld black holes
spread throughout the universe could produce similar interference effects; the
probability for "attolensing" may be non-negligible. If interference fringes
were observed, the fringe spacing would yield a simple upper limit on M.
Detection of a primordial black hole with M <~ 1e-19 Msun would challenge
general relativity and favor the braneworld model. Further work on lensing
tests of braneworld gravity must proceed into the physical optics regime, which
awaits a description of the full spacetime geometry around braneworld black
holes.Comment: 13 pages, 3 figures; accepted in PRD; expanded discussion of
prospects for observing attolensing with GLAS
Mathematics of Gravitational Lensing: Multiple Imaging and Magnification
The mathematical theory of gravitational lensing has revealed many generic
and global properties. Beginning with multiple imaging, we review
Morse-theoretic image counting formulas and lower bound results, and
complex-algebraic upper bounds in the case of single and multiple lens planes.
We discuss recent advances in the mathematics of stochastic lensing, discussing
a general formula for the global expected number of minimum lensed images as
well as asymptotic formulas for the probability densities of the microlensing
random time delay functions, random lensing maps, and random shear, and an
asymptotic expression for the global expected number of micro-minima. Multiple
imaging in optical geometry and a spacetime setting are treated. We review
global magnification relation results for model-dependent scenarios and cover
recent developments on universal local magnification relations for higher order
caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of
General Relativity and Gravitatio
On Multiple Einstein Rings
A number of recent surveys for gravitational lenses have found examples of
double Einstein rings. Here, we investigate analytically the occurrence of
multiple Einstein rings. We prove, under very general assumptions, that at most
one Einstein ring can arise from a mass distribution in a single plane lensing
a single background source. Two or more Einstein rings can therefore only occur
in multi-plane lensing. Surprisingly, we show that it is possible for a single
source to produce more than one Einstein ring. If two point masses (or two
isothermal spheres) in different planes are aligned with observer and source on
the optical axis, we show that there are up to three Einstein rings. We also
discuss the image morphologies for these two models if axisymmetry is broken,
and give the first instances of magnification invariants in the case of two
lens planes.Comment: MNRAS, in press (extra figure included
Aerosol microphysical impact on summertime convective precipitation in the Rocky Mountain region
We present an aerosol-cloud-precipitation modeling study of convective clouds using the Weather Research and Forecasting model fully coupled with Chemistry (WRF-Chem) version 3.1.1. Comparison of the model output with measurements from a research site in the Rocky Mountains in Colorado revealed that the fraction of organics in the model is underpredicted. This is most likely due to missing processes in the aerosol module in the model version used, such as new particle formation and growth of secondary organic aerosols. When boundary conditions and domain-wide initial conditions of aerosol loading are changed in the model (factors of 0.1, 0.2, and 10 of initial aerosol mass of SO4-2, NH4+, and NO3-), the domain-wide precipitation changes by about 5%. Analysis of the model results reveals that the Rocky Mountain region and Front Range environment is not conducive for convective invigoration to play a major role, in increasing precipitation, as seen in some other studies. When localized organic aerosol emission are increased to mimic new particle formation, the resulting increased aerosol loading leads to increases in domain-wide precipitation, opposite to what is seen in the model simulations with changed boundary and initial conditions
Gravitational Lensing by Rotating Naked Singularities
We model massive compact objects in galactic nuclei as stationary,
axially-symmetric naked singularities in the Einstein-massless scalar field
theory and study the resulting gravitational lensing. In the weak deflection
limit we study analytically the position of the two weak field images, the
corresponding signed and absolute magnifications as well as the centroid up to
post-Newtonian order. We show that there are a static post-Newtonian
corrections to the signed magnification and their sum as well as to the
critical curves, which are function of the scalar charge. The shift of the
critical curves as a function of the lens angular momentum is found, and it is
shown that they decrease slightingly for the weakly naked and vastly for the
strongly naked singularities with the increase of the scalar charge. The
point-like caustics drift away from the optical axis and do not depend on the
scalar charge. In the strong deflection limit approximation we compute
numerically the position of the relativistic images and their separability for
weakly naked singularities. All of the lensing quantities are compared to
particular cases as Schwarzschild and Kerr black holes as well as
Janis--Newman--Winicour naked singularities.Comment: 35 pages, 30 figure
Magnification relations in gravitational lensing via multidimensional residue integrals
We investigate the so-called magnification relations of gravitational lensing
models. We show that multidimensional residue integrals provide a simple
explanation for the existence of these relations, and an effective method of
computation. We illustrate the method with several examples, thereby deriving
new magnification relations for galaxy lens models and microlensing (point mass
lensing).Comment: 16 pages, uses revtex4, submitted to Journal of Mathematical Physic
Quasi-Equatorial Gravitational Lensing by Spinning Black Holes in the Strong Field Limit
Spherically symmetric black holes produce, by strong field lensing, two
infinite series of relativistic images, formed by light rays winding around the
black hole at distances comparable to the gravitational radius. In this paper,
we address the relevance of the black hole spin for the strong field lensing
phenomenology, focusing on trajectories close to the equatorial plane for
simplicity. In this approximation, we derive a two-dimensional lens equation
and formulae for the position and the magnification of the relativistic images
in the strong field limit. The most outstanding effect is the generation of a
non trivial caustic structure. Caustics drift away from the optical axis and
acquire finite extension. For a high enough black hole spin, depending on the
source extension, we can practically observe only one image rather than two
infinite series of relativistic images. In this regime, additional non
equatorial images may play an important role in the phenomenology.Comment: 13 pages, 9 figures. Improved version with detailed physical
discussio
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