56,290 research outputs found
Some Boas-Bellman Type Inequalities in 2-Inner Product Spaces
Some inequalities in 2-inner product spaces generalizing Bessel's result that
are similar to the Boas-Bellman inequality from inner product spaces, are
given. Applications for determinantal integral inequalities are also provided
Magnetic Helicity Conservation and Inverse Energy Cascade in Electron Magnetohydrodynamic Wave Packets
Electron magnetohydrodynamics (EMHD) provides a fluid-like description of
small-scale magnetized plasmas. An EMHD wave (also known as whistler wave)
propagates along magnetic field lines. The direction of propagation can be
either parallel or anti-parallel to the magnetic field lines. We numerically
study propagation of 3-dimensional (3D) EMHD wave packets moving in one
direction. We obtain two major results: 1. Unlike its magnetohydrodynamic (MHD)
counterpart, an EMHD wave packet is dispersive. Because of this, EMHD wave
packets traveling in one direction create opposite traveling wave packets via
self-interaction and cascade energy to smaller scales. 2. EMHD wave packets
traveling in one direction clearly exhibit inverse energy cascade. We find that
the latter is due to conservation of magnetic helicity. We compare inverse
energy cascade in 3D EMHD turbulence and 2-dimensional (2D) hydrodynamic
turbulence.Comment: Phys. Rev. Lett., accepted (4pages, 4 figures
Black hole quasinormal modes using the asymptotic iteration method
In this article we show that the asymptotic iteration method (AIM) allows one
to numerically find the quasinormal modes of Schwarzschild and Schwarzschild de
Sitter (SdS) black holes. An added benefit of the method is that it can also be
used to calculate the Schwarzschild anti-de Sitter (SAdS) quasinormal modes for
the case of spin zero perturbations. We also discuss an improved version of the
AIM, more suitable for numerical implementation.Comment: 10 pages, LaTeX; references added; substantially expanded versio
Graviton emission from simply rotating Kerr-de Sitter black holes: Transverse traceless tensor graviton modes
In this article we present results for tensor graviton modes (in seven
dimensions and greater, ) for greybody factors of Kerr-dS black holes
and for Hawking radiation from simply rotating (n+4)-dimensional Kerr black
holes. Although there is some subtlety with defining the Hawking temperature of
a Kerr-dS black hole, we present some preliminary results for emissions
assuming the standard Hawking normalization and a Bousso-Hawking-like
normalization.Comment: 12 pages, 18 figure
Spectral dimension of a quantum universe
In this paper, we calculate in a transparent way the spectral dimension of a
quantum spacetime, considering a diffusion process propagating on a fluctuating
manifold. To describe the erratic path of the diffusion, we implement a minimal
length by averaging the graininess of the quantum manifold in the flat space
case. As a result we obtain that, for large diffusion times, the quantum
spacetime behaves like a smooth differential manifold of discrete dimension. On
the other hand, for smaller diffusion times, the spacetime looks like a fractal
surface with a reduced effective dimension. For the specific case in which the
diffusion time has the size of the minimal length, the spacetime turns out to
have a spectral dimension equal to 2, suggesting a possible renormalizable
character of gravity in this regime. For smaller diffusion times, the spectral
dimension approaches zero, making any physical interpretation less reliable in
this extreme regime. We extend our result to the presence of a background field
and curvature. We show that in this case the spectral dimension has a more
complicated relation with the diffusion time, and conclusions about the
renormalizable character of gravity become less straightforward with respect to
what we found with the flat space analysis.Comment: 5 pages, 1 figure, references added, typos corrected, title changed,
final version published in Physical Review
Angular Eigenvalues of Higher-Dimensional Kerr-(A)dS Black Holes with Two Rotations
In this paper, following the work of Chen, L\"u and Pope, we present the
general metric for Kerr-(A)dS black holes with two rotations. The corresponding
Klein-Gordon equation is separated explicitly, from which we develop
perturbative expansions for the angular eigenvalues in powers of the rotation
parameters with .Comment: 10 pages, no figures. To appear in the proceedings of 2011 Shanghai
Asia-Pacific School and Workshop on Gravitatio
Bulk dominated fermion emission on a Schwarzschild background
Using the WKBJ approximation, and the Unruh method, we obtain semi-analytic
expressions for the absorption probability (in all energy regimes) for Dirac
fermions on a higher dimensional Schwarzschild background. We present an
analytic expression relating the absorption probability to the absorption
cross-section, and then use these results to plot the emission rates to third
order in the WKBJ approximation. The set-up we use is sufficiently general such
that it could also easily be applied to any spherically symmetric background in
-dimensions. Our results lead to the interesting conclusion that for
bulk fermion emission dominates brane localised emission. This is an example
contrary to the conjecture that black holes radiate mainly on the brane.Comment: 13 pages, 3 figure
Split fermion quasi-normal modes
In this paper we use the conformal properties of the spinor field to show how
we can obtain the fermion quasi-normal modes for a higher dimensional
Schwarzschild black hole. These modes are of interest in so called split
fermion models, where quarks and leptons are required to exist on different
branes in order to keep the proton stable. As has been previously shown, for
brane localized fields, the larger the number of dimensions the faster the
black hole damping rate. Moreover, we also present the analytic forms of the
quasi-normal frequencies in both the large angular momentum and the large mode
number limits.Comment: 11 pages, 7 figures, version 2 added reference
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