12,056 research outputs found
A Coloring Problem for Infinite Words
In this paper we consider the following question in the spirit of Ramsey
theory: Given where is a finite non-empty set, does there
exist a finite coloring of the non-empty factors of with the property that
no factorization of is monochromatic? We prove that this question has a
positive answer using two colors for almost all words relative to the standard
Bernoulli measure on We also show that it has a positive answer for
various classes of uniformly recurrent words, including all aperiodic balanced
words, and all words satisfying
for all sufficiently large, where denotes the number of
distinct factors of of length Comment: arXiv admin note: incorporates 1301.526
Analytic Kerr black hole lensing for equatorial observers in the strong deflection limit
In this paper we present an analytical treatment of gravitational lensing by
Kerr black holes in the limit of very large deflection angles, restricting to
observers in the equatorial plane. We accomplish our objective starting from
the Schwarzschild black hole and adding corrections up to second order in the
black hole spin. This is sufficient to provide a full description of all
caustics and the inversion of lens mapping for sources near them. On the basis
of these formulae we argue that relativistic images of Low Mass X-ray Binaries
around Sgr A* are very likely to be seen by future X-ray interferometry
missions.Comment: 19 pages, 9 figures, published on Phys. Rev.
The Ineludible non-Gaussianity of the Primordial Black Hole Abundance
We study the formation of primordial black holes when they are generated by
the collapse of large overdensities in the early universe. Since the density
contrast is related to the comoving curvature perturbation by a nonlinear
relation, the overdensity statistics is unavoidably non-Gaussian. We show that
the abundance of primordial black holes at formation may not be captured by a
perturbative approach which retains the first few cumulants of the non-Gaussian
probability distribution. We provide two techniques to calculate the
non-Gaussian abundance of primordial black holes at formation, one based on
peak theory and the other on threshold statistics. Our results show that the
unavoidable non-Gaussian nature of the inhomogeneities in the energy density
makes it harder to generate PBHs. We provide simple (semi-)analytical
expressions to calculate the non-Gaussian abundances of the primordial black
holes and show that for both narrow and broad power spectra the gaussian case
from threshold statistics is reproduced by increasing the amplitude of the
power spectrum by a factor .Comment: 26 pages, 10 figures, matching published versio
Testing Primordial Black Holes as Dark Matter through LISA
The idea that primordial black holes (PBHs) can comprise most of the dark
matter of the universe has recently reacquired a lot of momentum. Observational
constraints, however, rule out this possibility for most of the PBH masses,
with a notable exception around . These light PBHs may be
originated when a sizeable comoving curvature perturbation generated during
inflation re-enters the horizon during the radiation phase. During such a
stage, it is unavoidable that gravitational waves (GWs) are generated. Since
their source is quadratic in the curvature perturbations, these GWs are
generated fully non-Gaussian. Their frequency today is about the mHz, which is
exactly the range where the LISA mission has the maximum of its sensitivity.
This is certainly an impressive coincidence. We show that this scenario of PBHs
as dark matter can be tested by LISA by measuring the GW two-point correlator.
On the other hand, we show that the short observation time (as compared to the
age of the universe) and propagation effects of the GWs across the perturbed
universe from the production point to the LISA detector suppress the bispectrum
to an unobservable level. This suppression is completely general and not
specific to our model.Comment: 22 pages, 12 figures. v3: matching published versio
Kerr black hole lensing for generic observers in the strong deflection limit
We generalize our previous work on gravitational lensing by a Kerr black hole
in the strong deflection limit, removing the restriction to observers on the
equatorial plane. Starting from the Schwarzschild solution and adding
corrections up to the second order in the black hole spin, we perform a
complete analytical study of the lens equation for relativistic images created
by photons passing very close to a Kerr black hole. We find out that, to the
lowest order, all observables (including shape and shift of the black hole
shadow, caustic drift and size, images position and magnification) depend on
the projection of the spin on a plane orthogonal to the line of sight. In order
to break the degeneracy between the black hole spin and its inclination
relative to the observer, it is necessary to push the expansion to higher
orders. In terms of future VLBI observations, this implies that very accurate
measures are needed to determine these two parameters separately.Comment: 17 pages, 4 figures, one section added, to appear on Physical Review
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Quantum spin Hall effect in bound states in continuum
Moving the polarization of the incident wave along a meridian of the Poincaré sphere, experimentally we show that the coupling with the fundamental Bloch's surface waves of the mode, provide a spatially coherent, macroscopic spinmomentum locked propagation along the symmetry axes of the PhCM. This novel mechanism of light-spin manipulation enables a versatile implementation of spin-optical structures that may pave the way to novel strategies for light spin technology and photonic multiplatform implementations
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