168 research outputs found
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
Gravitational lensing in braneworld gravity: formalism and applications
In this article, we develop a formalism which is different from the standard
lensing scenario and is necessary for understanding lensing by gravitational
fields which arise as solutions of the effective Einstein equations on the
brane. We obtain general expressions for measurable quantities such as time
delay, deflection angle, Einstein ring and magnification. Subsequently, we
estimate the deviations (relative to the standard lensing scenario) in the
abovementioned quantities by considering the line elements for clusters and
spiral galaxies obtained by solving the effective Einstein equations on the
brane. Our analysis reveals that gravitational lensing can be a useful tool for
testing braneworld gravity as well as the existence of extra dimensions.Comment: 20 pages, 1 figure, 2 tables. Accepted for publication in Classical
and Quantum Gravit
Wavefronts, Caustic Sheets, and Caustic Surfing in Gravitational Lensing
Very little attention has been paid to the properties of optical wavefronts
and caustic surfaces due to gravitational lensing. Yet the wavefront-based
point of view is natural and provides insights into the nature of the caustic
surfaces on a gravitationally lensed lightcone. We derive analytically the
basic equations governing the wavefronts, lightcones, caustics on wavefronts,
and caustic surfaces on lightcones in the context of weak-field, thin-screen
gravitational lensing. These equations are all related to the potential of the
lens. In the process, we also show that the standard single-plane gravitational
lensing map extends to a new mapping, which we call a wavefront lensing map.
Unlike the standard lensing map, the Jacobian matrix of a wavefront lensing map
is not symmetric. Our formulas are then applied to caustic ``surfing.'' By
surfing a caustic surface, a space-borne telescope can be fixed on a
gravitationally lensed source to obtain an observation of the source at very
high magnification over an extended time period, revealing structure about the
source that could not otherwise be resolved. Using our analytical expressions
for caustic sheets, we present a scheme for surfing a caustic sheet of a lensed
source in rectilinear motion. Detailed illustrations are also presented of the
possible types of wavefronts and caustic sheets due to nonsingular and singular
elliptical potentials, and singular isothermal spheres, including an example of
caustic surfing for a singular elliptical potential lens.Comment: To appear in J. Math. Phys., 31 pages, 15 figure
Gravitational Lensing and f(R) theories in the Palatini approach
We investigate gravitational lensing in the Palatini approach to the f(R)
extended theories of gravity. Starting from an exact solution of the f(R) field
equations, which corresponds to the Schwarzschild-de Sitter metric and, on the
basis of recent studies on this metric, we focus on some lensing observables,
in order to evaluate the effects of the non linearity of the gravity
Lagrangian. We give estimates for some astrophysical events, and show that
these effects are tiny for galactic lenses, but become interesting for
extragalactic ones.Comment: 7 Pages, RevTex, 1 eps figure; references added; revised to match the
version accepted for publication in General Relativity and Gravitatio
A Minimal Threshold of c-di-GMP Is Essential for Fruiting Body Formation and Sporulation in Myxococcus xanthus
Generally, the second messenger bis-(3’-5’)-cyclic dimeric GMP (c-di-GMP) regulates the switch between motile and sessile lifestyles in bacteria. Here, we show that c-di-GMP is an essential regulator of multicellular development in the social bacterium Myxococcus xanthus. In response to starvation, M. xanthus initiates a developmental program that culminates in formation of spore-filled fruiting bodies. We show that c-di-GMP accumulates at elevated levels during development and that this increase is essential for completion of development whereas excess c-di-GMP does not interfere with development. MXAN3735 (renamed DmxB) is identified as a diguanylate cyclase that only functions during development and is responsible for this increased c-di-GMP accumulation. DmxB synthesis is induced in response to starvation, thereby restricting DmxB activity to development. DmxB is essential for development and functions downstream of the Dif chemosensory system to stimulate exopolysaccharide accumulation by inducing transcription of a subset of the genes encoding proteins involved in exopolysaccharide synthesis. The developmental defects in the dmxB mutant are non-cell autonomous and rescued by co-development with a strain proficient in exopolysaccharide synthesis, suggesting reduced exopolysaccharide accumulation as the causative defect in this mutant. The NtrC-like transcriptional regulator EpsI/Nla24, which is required for exopolysaccharide accumulation, is identified as a c-diGMP receptor, and thus a putative target for DmxB generated c-di-GMP. Because DmxB can be—at least partially—functionally replaced by a heterologous diguanylate cyclase, these results altogether suggest a model in which a minimum threshold level of c-di-GMP is essential for the successful completion of multicellular development in M. xanthus
Gravitational Lensing
Gravitational lensing has developed into one of the most powerful tools for
the analysis of the dark universe. This review summarises the theory of
gravitational lensing, its main current applications and representative results
achieved so far. It has two parts. In the first, starting from the equation of
geodesic deviation, the equations of thin and extended gravitational lensing
are derived. In the second, gravitational lensing by stars and planets,
galaxies, galaxy clusters and large-scale structures is discussed and
summarised.Comment: Invited review article to appear in Classical and Quantum Gravity, 85
pages, 15 figure
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