86,975 research outputs found
Weak Gravitational Lensing in Fourth Order Gravity
For a general class of analytic
we discuss the gravitational lensing in the Newtonian Limit of theory. From the
properties of Gauss Bonnet invariant it is successful to consider only two
curvature invariants between the Ricci and Riemann tensor. Then we analyze the
dynamics of photon embedded in a gravitational field of a generic
-Gravity. The metric is time independent
and spherically symmetric. The metric potentials are Schwarzschild-like, but
there are two additional Yukawa terms linked to derivatives of with respect
to two curvature invariants. Considering the case of a point-like lens, and
after of a generic matter distribution of lens, we study the deflection angle
and the images angular position. Though the additional Yukawa terms in the
gravitational potential modifies dynamics with respect to General Relativity,
the geodesic trajectory of photon is unaffected by the modification in the
action by only . While we find different results (deflection angle
smaller than one of General Relativity) only thank to introduction of a generic
function of Ricci tensor square. Finally we can affirm the lensing phenomena
for all -Gravities are equal to the ones known from General Relativity.
We conclude the paper showing and comparing the deflection angle and image
positions for -Gravity with respect to
ones of General Relativity.Comment: 11 pages, 5 figure
Evolution method and "differential hierarchy" of colored knot polynomials
We consider braids with repeating patterns inside arbitrary knots which
provides a multi-parametric family of knots, depending on the "evolution"
parameter, which controls the number of repetitions. The dependence of knot
(super)polynomials on such evolution parameters is very easy to find. We apply
this evolution method to study of the families of knots and links which include
the cases with just two parallel and anti-parallel strands in the braid, like
the ordinary twist and 2-strand torus knots/links and counter-oriented 2-strand
links. When the answers were available before, they are immediately reproduced,
and an essentially new example is added of the "double braid", which is a
combination of parallel and anti-parallel 2-strand braids. This study helps us
to reveal with the full clarity and partly investigate a mysterious
hierarchical structure of the colored HOMFLY polynomials, at least, in
(anti)symmetric representations, which extends the original observation for the
figure-eight knot to many (presumably all) knots. We demonstrate that this
structure is typically respected by the t-deformation to the superpolynomials.Comment: 31 page
Gaussian distribution of LMOV numbers
Recent advances in knot polynomial calculus allowed us to obtain a huge
variety of LMOV integers counting degeneracy of the BPS spectrum of topological
theories on the resolved conifold and appearing in the genus expansion of the
plethystic logarithm of the Ooguri-Vafa partition functions. Already the very
first look at this data reveals that the LMOV numbers are randomly distributed
in genus (!) and are very well parameterized by just three parameters depending
on the representation, an integer and the knot. We present an accurate
formulation and evidence in support of this new puzzling observation about the
old puzzling quantities. It probably implies that the BPS states, counted by
the LMOV numbers can actually be composites made from some still more
elementary objects.Comment: 23 page
INTWORLSA President\u27s Report on the Addis Ababa Seminar: Human Rights and the Police and Internal Security Forces in Certain African Countries
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