Asymptotic Quasinormal Frequencies for Black Holes in Non-Asymptotically Flat Spacetimes

The exact computation of asymptotic quasinormal frequencies is a technical problem which involves the analytic continuation of a Schrodinger-like equation to the complex plane and then performing a method of monodromy matching at the several poles in the plane. While this method was successfully used in asymptotically flat spacetime, as applied to both the Schwarzschild and Reissner-Nordstrom solutions, its extension to non-asymptotically flat spacetimes has not been achieved yet. In this work it is shown how to extend the method to this case, with the explicit analysis of Schwarzschild de Sitter and large Schwarzschild Anti-de Sitter black holes, both in four dimensions. We obtain, for the first time, analytic expressions for the asymptotic quasinormal frequencies of these black hole spacetimes, and our results match previous numerical calculations with great accuracy. We also list some results concerning the general classification of asymptotic quasinormal frequencies in d-dimensional spacetimes.Comment: JHEP3.cls, 20 pages, 5 figures; v2: added references, typos corrected, minor changes, final version for JMP; v3: more typos fixe

Painleve-Gullstrand Coordinates for the Kerr Solution

We construct a coordinate system for the Kerr solution, based on the zero angular momentum observers dropped from infinity, which generalizes the Painleve-Gullstrand coordinate system for the Schwarzschild solution. The Kerr metric can then be interpreted as describing space flowing on a (curved) Riemannian 3-manifold. The stationary limit arises as the set of points on this manifold where the speed of the flow equals the speed of light, and the horizons as the set of points where the radial speed equals the speed of light. A deeper analysis of what is meant by the flow of space reveals that the acceleration of free-falling objects is generally not in the direction of this flow. Finally, we compare the new coordinate system with the closely related Doran coordinate system.Comment: 6 pages; v2: new section, matches final published version; v3: sign error in the expression of the function delta correcte

Clinical and Pathological Findings in Women with Fabry Disease

Introduction. Fabry disease is a rare metabolic disorder caused by the genetic deficiency of the lysosomal hydrolase alpha-galactosidase A, located on chromosome X. Females with the defective gene are more than carriers and can develop a wide range of symptoms. Nevertheless, disease symptoms generally occur later and are less severe in women than in men. The enzyme deficiency manifests as a glycosphingolipidosis with progressive accumulation of glycosphingolipids and deposit of inclusion bodies in lysosomes giving a myelinlike appearance. Patients and Methods. Records of renal biopsies performed on adults from 1st January 2008 to 31st August 2011, were retrospectively examined at the Renal Pathology Laboratory. We retrieved biopsies diagnosed with Fabry disease and reviewed clinical and laboratory data and pathology findings. Results. Four female patients with a mean age of 49.3±4.5 (44-55) years were identified. The mean proteinuria was 0.75±0.3 g/24h (0.4-1.2) and estimated glomerular filtration rate (CKD EPI equation) was 71±15.7 ml/min/1.73m2 (48-83). Three patients experienced extra-renal organ involvement (cerebrovascular, cardiac, dermatologic, ophthalmologic and thyroid) with distinct severity degrees. Leukocyte α-GAL A activity was below normal range in the four cases but plasma and urinary enzymatic activity was normal. Light microscopy showed predominant vacuolisation of the podocyte cytoplasm and darkly staining granular inclusions on paraffin and plastic-embedded semi-thin sections. Electron microscopy showed in three patients the characteristic myelin-like inclusions in the podocyte cytoplasm and also focal podocyte foot process effacement. In one case the inclusions were also present in parietal glomerular cells, endothelial cells of peritubular capillary and arterioles. Conclusion. Clinical signs and symptoms are varied and can be severe among heterozygous females with Fabry disease. Intracellular accumulation of glycosphingolipids is a characteristic histologic finding of Fabry nephropathy. Since this disease is a potentially treatable condition, its early identification is imperative. We should consider it in the differential diagnosis of any patient presenting with proteinuria and/or chronic kidney disease, especially if there is a family history of kidney disease

Higher-Derivative Corrected Black Holes: Perturbative Stability and Absorption Cross-Section in Heterotic String Theory

This work addresses spherically symmetric, static black holes in higher-derivative stringy gravity. We focus on the curvature-squared correction to the Einstein-Hilbert action, present in both heterotic and bosonic string theory. The string theory low-energy effective action necessarily describes both a graviton and a dilaton, and we concentrate on the Callan-Myers-Perry solution in d-dimensions, describing stringy corrections to the Schwarzschild geometry. We develop the perturbation theory for the higher-derivative corrected action, along the guidelines of the Ishibashi-Kodama framework, focusing on tensor type gravitational perturbations. The potential obtained allows us to address the perturbative stability of the black hole solution, where we prove stability in any dimension. The equation describing gravitational perturbations to the Callan-Myers-Perry geometry also allows for a study of greybody factors and quasinormal frequencies. We address gravitational scattering at low frequencies, computing corrections arising from the curvature-squared term in the stringy action. We find that the absorption cross-section receives \alpha' corrections, even though it is still proportional to the area of the black hole event-horizon. We also suggest an expression for the absorption cross-section which could be valid to all orders in \alpha'.Comment: JHEP3.cls, 29 pages; v2: added refs, minor corrections and additions; v3: added more refs, more minor corrections and addition

Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications

Selected papers of the 17th Congress of the Portuguese Statistical Society, covering recent advances in Statistics, particularly in Regression, Extreme values, Markov processes and statistical applications in several areas

Quasinormal ringing of Kerr black holes: The excitation factors

Distorted black holes radiate gravitational waves. In the so-called ringdown phase radiation is emitted in a discrete set of complex quasinormal frequencies, whose values depend only on the black hole's mass and angular momentum. Ringdown radiation could be detectable with large signal-to-noise ratio by the Laser Interferometer Space Antenna LISA. If more than one mode is detected, tests of the black hole nature of the source become possible. The detectability of different modes depends on their relative excitation, which in turn depends on the cause of the perturbation (i.e. on the initial data). A ``universal'', initial data-independent measure of the relative mode excitation is encoded in the poles of the Green's function that propagates small perturbations of the geometry (``excitation factors''). We compute for the first time the excitation factors for general-spin perturbations of Kerr black holes. We find that for corotating modes with $l=m$ the excitation factors tend to zero in the extremal limit, and that the contribution of the overtones should be more significant when the black hole is fast rotating. We also present the first analytical calculation of the large-damping asymptotics of the excitation factors for static black holes, including the Schwarzschild and Reissner-Nordstrom metrics. This is an important step to determine the convergence properties of the quasinormal mode expansion.Comment: 33 pages, 9 figures, 7 tables, RevTeX4. v2: Two new figures and minor changes in the presentation. Matches version in press in Phys. Rev.

Perturbations of anti-de Sitter black holes

I review perturbations of black holes in asymptotically anti-de Sitter space. I show how the quasi-normal modes governing these perturbations can be calculated analytically and discuss the implications on the hydrodynamics of gauge theory fluids per the AdS/CFT correspondence. I also discuss phase transitions of hairy black holes with hyperbolic horizons and the dual superconductors emphasizing the analytical calculation of their properties.Comment: 25 pages, 4 figures, prepared for the proceedings of the 5th Aegean Summer School "From Gravity to Thermal Gauge Theories: the AdS/CFT Correspondence," Milos, Greece, September 2009

A river model of space

Within the theory of general relativity gravitational phenomena are usually attributed to the curvature of four-dimensional spacetime. In this context we are often confronted with the question of how the concept of ordinary physical three-dimensional space fits into this picture. In this work we present a simple and intuitive model of space for both the Schwarzschild spacetime and the de Sitter spacetime in which physical space is defined as a specified set of freely moving reference particles. Using a combination of orthonormal basis fields and the usual formalism in a coordinate basis we calculate the physical velocity field of these reference particles. Thus we obtain a vivid description of space in which space behaves like a river flowing radially toward the singularity in the Schwarzschild spacetime and radially toward infinity in the de Sitter spacetime. We also consider the effect of the river of space upon light rays and material particles and show that the river model of space provides an intuitive explanation for the behavior of light and particles at and beyond the event horizons associated with these spacetimes.Comment: 22 pages, 5 figure

Phase-space and Black Hole Entropy of Higher Genus Horizons in Loop Quantum Gravity

In the context of loop quantum gravity, we construct the phase-space of isolated horizons with genus greater than 0. Within the loop quantum gravity framework, these horizons are described by genus g surfaces with N punctures and the dimension of the corresponding phase-space is calculated including the genus cycles as degrees of freedom. From this, the black hole entropy can be calculated by counting the microstates which correspond to a black hole of fixed area. We find that the leading term agrees with the A/4 law and that the sub-leading contribution is modified by the genus cycles.Comment: 22 pages, 9 figures. References updated. Minor changes to match version to appear in Class. Quant. Gra

Mathisson's helical motions for a spinning particle --- are they unphysical?

It has been asserted in the literature that Mathisson's helical motions are unphysical, with the argument that their radius can be arbitrarily large. We revisit Mathisson's helical motions of a free spinning particle, and observe that such statement is unfounded. Their radius is finite and confined to the disk of centroids. We argue that the helical motions are perfectly valid and physically equivalent descriptions of the motion of a spinning body, the difference between them being the choice of the representative point of the particle, thus a gauge choice. We discuss the kinematical explanation of these motions, and we dynamically interpret them through the concept of hidden momentum. We also show that, contrary to previous claims, the frequency of the helical motions coincides, even in the relativistic limit, with the zitterbewegung frequency of the Dirac equation for the electron