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, $n\geq 3$) 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 $D\geq 6$.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 $d$-dimensions. Our results lead to the interesting conclusion that for $d>5$ 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