The optic nerve: a new window into cerebrospinal fluid composition?

Cerebrospinal fluid (CSF) pressure and composition are generally thought to be homogeneous within small limits throughout all CSF compartments. CSF sampled during lumbar puncture therefore should be representative for all CSF compartments. On the basis of clinical findings, histology and biochemical markers, we present for the first time strong evidence that the subarachnoid spaces (SAS) of the optic nerve (ON) can become separated from other CSF compartments in certain ON disorders, thus leading to an ON sheath compartment syndrome. This may result in an abnormal concentration gradient of CSF molecular markers determined in locally sampled CSF compared with CSF taken during lumbar punctur

Solutions to Maxwell's Equations using Spheroidal Coordinates

Analytical solutions to the wave equation in spheroidal coordinates in the short wavelength limit are considered. The asymptotic solutions for the radial function are significantly simplified, allowing scalar spheroidal wave functions to be defined in a form which is directly reminiscent of the Laguerre-Gaussian solutions to the paraxial wave equation in optics. Expressions for the Cartesian derivatives of the scalar spheroidal wave functions are derived, leading to a new set of vector solutions to Maxwell's equations. The results are an ideal starting point for calculations of corrections to the paraxial approximation

Perturbations in the Kerr-Newman Dilatonic Black Hole Background: I. Maxwell waves

In this paper we analyze the perturbations of the Kerr-Newman dilatonic black hole background. For this purpose we perform a double expansion in both the background electric charge and the wave parameters of the relevant quantities in the Newman-Penrose formalism. We then display the gravitational, dilatonic and electromagnetic equations, which reproduce the static solution (at zero order in the wave parameter) and the corresponding wave equations in the Kerr background (at first order in the wave parameter and zero order in the electric charge). At higher orders in the electric charge one encounters corrections to the propagations of waves induced by the presence of a non-vanishing dilaton. An explicit computation is carried out for the electromagnetic waves up to the asymptotic form of the Maxwell field perturbations produced by the interaction with dilatonic waves. A simple physical model is proposed which could make these perturbations relevant to the detection of radiation coming from the region of space near a black hole.Comment: RevTeX, 36 pages in preprint style, 1 figure posted as a separate PS file, submitted to Phys. Rev.

Evaporation of a Kerr black hole by emission of scalar and higher spin particles

We study the evolution of an evaporating rotating black hole, described by the Kerr metric, which is emitting either solely massless scalar particles or a mixture of massless scalar and nonzero spin particles. Allowing the hole to radiate scalar particles increases the mass loss rate and decreases the angular momentum loss rate relative to a black hole which is radiating nonzero spin particles. The presence of scalar radiation can cause the evaporating hole to asymptotically approach a state which is described by a nonzero value of $a_* \equiv a / M$. This is contrary to the conventional view of black hole evaporation, wherein all black holes spin down more rapidly than they lose mass. A hole emitting solely scalar radiation will approach a final asymptotic state described by $a_* \simeq 0.555$. A black hole that is emitting scalar particles and a canonical set of nonzero spin particles (3 species of neutrinos, a single photon species, and a single graviton species) will asymptotically approach a nonzero value of $a_*$ only if there are at least 32 massless scalar fields. We also calculate the lifetime of a primordial black hole that formed with a value of the rotation parameter $a_{*}$, the minimum initial mass of a primordial black hole that is seen today with a rotation parameter $a_{*}$, and the entropy of a black hole that is emitting scalar or higher spin particles.Comment: 22 pages, 13 figures, RevTeX format; added clearer descriptions for variables, added journal referenc

Brane decay of a (4+n)-dimensional rotating black hole: spin-0 particles

In this work, we study the `scalar channel' of the emission of Hawking radiation from a (4+n)-dimensional, rotating black hole on the brane. We numerically solve both the radial and angular part of the equation of motion for the scalar field, and determine the exact values of the absorption probability and of the spheroidal harmonics, respectively. With these, we calculate the particle, energy and angular momentum emission rates, as well as the angular variation in the flux and power spectra -- a distinctive feature of emission during the spin-down phase of the life of the produced black hole. Our analysis is free from any approximations, with our results being valid for arbitrarily large values of the energy of the emitted particle, angular momentum of the black hole and dimensionality of spacetime. We finally compute the total emissivities for the number of particles, energy and angular momentum and compare their relative behaviour for different values of the parameters of the theory.Comment: 24 pages, 13 figure

Greybody Factors for Brane Scalar Fields in a Rotating Black-Hole Background

We study the evaporation of (4+n)-dimensional rotating black holes into scalar degrees of freedom on the brane. We calculate the corresponding absorption probabilities and cross-sections obtaining analytic solutions in the low-energy regime, and compare the derived analytic expressions to numerical results, with very good agreement. We then consider the high-energy regime, construct an analytic high-energy solution to the scalar-field equation by employing a new method, and calculate the absorption probability and cross-section for this energy regime, finding again a very good agreement with the exact numerical results. We also determine the high-energy asymptotic value of the total cross-section, and compare it to the analytic results derived from the application of the geometrical optics limit.Comment: Latex file, 30 pages, 5 figures, typos corrected, version published in Phys. Rev.

High Frequency Asymptotics for the Spin-Weighted Spheroidal Equation

We fully determine a uniformly valid asymptotic behaviour for large $a \omega$ and fixed $m$ of the angular solutions and eigenvalues of the spin-weighted spheroidal differential equation. We fully complement the analytic work with a numerical study.Comment: The .tar.gz file should contain 1 tex file, 24 figures in .ps format and 1 bibliography file in .bbl format. All these files are located in the same director

Cerebrospinal fluid dynamics between the intracranial and the subarachnoid space of the optic nerve. Is it always bidirectional?

CSF is thought to flow continuously from the site of production in the ventricles into interconnected spaces; i.e. cisterns and subarachnoid spaces (SASs). Since the SAS of the optic nerve is defined by a cul-de-sac anatomy, it is not evident how local CSF might recycle from that region to the general SAS. The concept of free communication of CSF has recently been challenged by the description of a concentration gradient of beta-trace protein, a lipocalin-like prostaglandin d-synthase (L-PGDS), between the spinal CSF and that in the SAS of the optic nerve, indicating diminished local clearance or local overproduction of L-PGDS here. In fact, computed cisternography with a contrast agent in three patients with idiopathic intracranial hypertension and asymmetric papilloedema demonstrate a lack of contrast-loaded CSF in the SAS of the optic nerve despite it being present in the intracranial SAS, thus suggesting compartmentation of the SAS of the optic nerve. The concept of an optic nerve compartment syndrome is further supported by a concentration gradient of brain-derived L-PGDS between the spinal CSF and the CSF from the optic nerve SAS in the same patient

Asymptotic Spectroscopy of Rotating Black Holes

We calculate analytically the transmission and reflection amplitudes for waves incident on a rotating black hole in d=4, analytically continued to asymptotically large, nearly imaginary frequency. These amplitudes determine the asymptotic resonant frequencies of the black hole, including quasinormal modes, total-transmission modes and total-reflection modes. We identify these modes with semiclassical bound states of a one-dimensional Schrodinger equation, localized along contours in the complexified r-plane which connect turning points of corresponding null geodesics. Each family of modes has a characteristic temperature and chemical potential. The relations between them provide hints about the microscopic description of the black hole in this asymptotic regime.Comment: References adde

Intermediate Asymptotics of the Kerr Quasinormal Spectrum

We study analytically the quasinormal mode spectrum of near-extremal (rotating) Kerr black holes. We find an analytic expression for these black-hole resonances in terms of the black-hole physical parameters: its Bekenstein-Hawking temperature T_{BH} and its horizon's angular velocity \Omega, which is valid in the intermediate asymptotic regime 1<<\omega<<1/T_{BH}.Comment: 4 page