7 research outputs found
Light's Bending Angle due to Black Holes: From the Photon Sphere to Infinity
The bending angle of light is a central quantity in the theory of
gravitational lensing. We develop an analytical perturbation framework for
calculating the bending angle of light rays lensed by a Schwarzschild black
hole. Using a perturbation parameter given in terms of the gravitational radius
of the black hole and the light ray's impact parameter, we determine an
invariant series for the strong-deflection bending angle that extends beyond
the standard logarithmic deflection term used in the literature. In the
process, we discovered an improvement to the standard logarithmic deflection
term. Our perturbation framework is also used to derive as a consistency check,
the recently found weak deflection bending angle series. We also reformulate
the latter series in terms of a more natural invariant perturbation parameter,
one that smoothly transitions between the weak and strong deflection series. We
then compare our invariant strong deflection bending-angle series with the
numerically integrated exact formal bending angle expression, and find less
than 1% discrepancy for light rays as far out as twice the critical impact
parameter. The paper concludes by showing that the strong and weak deflection
bending angle series together provide an approximation that is within 1% of the
exact bending angle value for light rays traversing anywhere between the photon
sphere and infinity.Comment: 22 pages, 5 figure
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
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
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
Gravitational Lensing by Black Holes
We review the theoretical aspects of gravitational lensing by black holes,
and discuss the perspectives for realistic observations. We will first treat
lensing by spherically symmetric black holes, in which the formation of
infinite sequences of higher order images emerges in the clearest way. We will
then consider the effects of the spin of the black hole, with the formation of
giant higher order caustics and multiple images. Finally, we will consider the
perspectives for observations of black hole lensing, from the detection of
secondary images of stellar sources and spots on the accretion disk to the
interpretation of iron K-lines and direct imaging of the shadow of the black
hole.Comment: Invited article for the GRG special issue on lensing (P. Jetzer, Y.
Mellier and V. Perlick Eds.). 31 pages, 12 figure
Bounds on number of cusps due to point mass gravitational lenses
The total number of cusps, N_c_u_s_p_s, due to g point masses on a single plane having non-normalized external shear #gamma# > 0 and continuously matter with constant density #sigma#_c, is proven to be bounded as follows: 0 #<=# N_c_u_s_p_s #<=# 12g"2. For vanishing shear #gamma# = 0 we obtain the result 0 #<=# N_c_u_s_p_s #<=# 12g(g-1). Consequences of these bounds for the global geometry of caustics are discussed. It is also shown that if #gamma# ge 0 and #sigma#_c is sufficiently large, then all cusps can be eliminated, that is, N_c_u_s_p_s = 0. The methods of the paper are based on a new approach to point-mass gravitational lensing using complex quantities and the theory of resultants. (orig.)Available from TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman