Order statistics of 1/f^{\alpha} signals

Order statistics of periodic, Gaussian noise with 1/f^{\alpha} power spectrum is investigated. Using simulations and phenomenological arguments, we find three scaling regimes for the average gap d_k= between the k-th and (k+1)-st largest values of the signal. The result d_k ~ 1/k known for independent, identically distributed variables remains valid for 0<\alpha<1. Nontrivial, \alpha-dependent scaling exponents d_k ~ k^{(\alpha -3)/2} emerge for 1<\alpha<5 and, finally, \alpha-independent scaling, d_k ~ k is obtained for \alpha>5. The spectra of average ordered values \epsilon_k= ~ k^{\beta} is also examined. The exponent {\beta} is derived from the gap scaling as well as by relating \epsilon_k to the density of near extreme states. Known results for the density of near extreme states combined with scaling suggest that \beta(\alpha=2)=1/2, \beta(4)=3/2, and beta(infinity)=2 are exact values. We also show that parallels can be drawn between \epsilon_k and the quantum mechanical spectra of a particle in power-law potentials.Comment: 8 pages, 5 figure

Maxwell Fields in Spacetimes Admitting Non-Null Killing Vectors

We consider source-free electromagnetic fields in spacetimes possessing a non-null Killing vector field, $\xi^a$. We assume further that the electromagnetic field tensor, $F_{ab}$, is invariant under the action of the isometry group induced by $\xi^a$. It is proved that whenever the two potentials associated with the electromagnetic field are functionally independent the entire content of Maxwell's equations is equivalent to the relation \n^aT_{ab}=0. Since this relation is implied by Einstein's equation we argue that it is enough to solve merely Einstein's equation for these electrovac spacetimes because the relevant equations of motion will be satisfied automatically. It is also shown that for the exceptional case of functionally related potentials \n^aT_{ab}=0 implies along with one of the relevant equations of motion that the complementary equation concerning the electromagnetic field is satisfied.Comment: 7 pages,PACS numbers: 04.20.Cv, 04.20.Me, 04.40.+

Large scale numerical simulations of "ultrametric" long-range depinning

The depinning of an elastic line interacting with a quenched disorder is studied for long range interactions, applicable to crack propagation or wetting. An ultrametric distance is introduced instead of the Euclidean distance, allowing for a drastic reduction of the numerical complexity of the problem. Based on large scale simulations, two to three orders of magnitude larger than previously considered, we obtain a very precise determination of critical exponents which are shown to be indistinguishable from their Euclidean metric counterparts. Moreover the scaling functions are shown to be unchanged. The choice of an ultrametric distance thus does not affect the universality class of the depinning transition and opens the way to an analytic real space renormalization group approach.Comment: submitted to Phys. Rev.

Black Holes in Einstein-Aether Theory

We study black hole solutions in general relativity coupled to a unit timelike vector field dubbed the "aether". To be causally isolated a black hole interior must trap matter fields as well as all aether and metric modes. The theory possesses spin-0, spin-1, and spin-2 modes whose speeds depend on four coupling coefficients. We find that the full three-parameter family of local spherically symmetric static solutions is always regular at a metric horizon, but only a two-parameter subset is regular at a spin-0 horizon. Asymptotic flatness imposes another condition, leaving a one-parameter family of regular black holes. These solutions are compared to the Schwarzschild solution using numerical integration for a special class of coupling coefficients. They are very close to Schwarzschild outside the horizon for a wide range of couplings, and have a spacelike singularity inside, but differ inside quantitatively. Some quantities constructed from the metric and aether oscillate in the interior as the singularity is approached. The aether is at rest at spatial infinity and flows into the black hole, but differs significantly from the the 4-velocity of freely-falling geodesics.Comment: 22 pages, 6 figures; v2: minor editing; v3: corrected overall sign in twist formula and an error in the equation for the aether stress tensor. Results unchanged since correct form was used in calculations; v4: corrected minor typ

Global Extensions of Spacetimes Describing Asymptotic Final States of Black Holes

We consider a globally hyperbolic, stationary spacetime containing a black hole but no white hole. We assume, further, that the event horizon, \tn, of the black hole is a Killing horizon with compact cross-sections. We prove that if surface gravity is non-zero constant throughout the horizon one can {\it globally} extend such a spacetime so that the image of $\cal N$ is a proper subset of a regular bifurcate Killing horizon in the enlarged spacetime. The necessary and sufficient conditions are given for the extendibility of matter fields to the enlarged spacetime. These conditions are automatically satisfied if the spacetime is static (and, hence ``$t$"-reflection symmetric) or stationary-axisymmetric with ``$t-\phi$" reflection isometry and the matter fields respect the reflection isometry. In addition, we prove that a necessary and sufficient condition for the constancy of the surface gravity on a Killing horizon is that the exterior derivative of the twist of the horizon Killing field vanish on the horizon. As a corollary of this, we recover a result of Carter that constancy of surface gravity holds for any black hole which is static or stationary- axisymmetric with the ``$t-\phi$" reflection isometry. No use of Einstein's equation is made in obtaining any of the above results. Taken together, these results support the view that any spacetime representing the asymptotic final state of a black hole formed by gravitational collapse may be assumed to possess a bifurcate Killing horizon or a Killing horizon with vanishing surface gravity.Comment: 20 pages, plain te

On smoothness of Black Saturns

We prove smoothness of the domain of outer communications (d.o.c.) of the Black Saturn solutions of Elvang and Figueras. We show that the metric on the d.o.c. extends smoothly across two disjoint event horizons with topology R x S^3 and R x S^1 x S^2. We establish stable causality of the d.o.c. when the Komar angular momentum of the spherical component of the horizon vanishes, and present numerical evidence for stable causality in general.Comment: 47 pages, 5 figure

Agrp neuron activity is required for alcohol-induced overeating

Alcohol intake associates with overeating in humans. This overeating is a clinical concern, but its causes are puzzling, because alcohol (ethanol) is a calorie-dense nutrient, and calorie intake usually suppresses brain appetite signals. The biological factors necessary for ethanol-induced overeating remain unclear, and societal causes have been proposed. Here we show that core elements of the brain’s feeding circuits—the hypothalamic Agrp neurons that are normally activated by starvation and evoke intense hunger—display electrical and biochemical hyperactivity on exposure to dietary doses of ethanol in brain slices. Furthermore, by circuit-specific chemogenetic interference in vivo, we find that the Agrp cell activity is essential for ethanol-induced overeating in the absence of societal factors, in single-housed mice. These data reveal how a widely consumed nutrient can paradoxically sustain brain starvation signals, and identify a biological factor required for appetite evoked by alcohol

Spacetimes foliated by Killing horizons

It seems to be expected, that a horizon of a quasi-local type, like a Killing or an isolated horizon, by analogy with a globally defined event horizon, should be unique in some open neighborhood in the spacetime, provided the vacuum Einstein or the Einstein-Maxwell equations are satisfied. The aim of our paper is to verify whether that intuition is correct. If one can extend a so called Kundt metric, in such a way that its null, shear-free surfaces have spherical spacetime sections, the resulting spacetime is foliated by so called non-expanding horizons. The obstacle is Kundt's constraint induced at the surfaces by the Einstein or the Einstein-Maxwell equations, and the requirement that a solution be globally defined on the sphere. We derived a transformation (reflection) that creates a solution to Kundt's constraint out of data defining an extremal isolated horizon. Using that transformation, we derived a class of exact solutions to the Einstein or Einstein-Maxwell equations of very special properties. Each spacetime we construct is foliated by a family of the Killing horizons. Moreover, it admits another, transversal Killing horizon. The intrinsic and extrinsic geometry of the transversal Killing horizon coincides with the one defined on the event horizon of the extremal Kerr-Newman solution. However, the Killing horizon in our example admits yet another Killing vector tangent to and null at it. The geometries of the leaves are given by the reflection.Comment: LaTeX 2e, 13 page

Quasi-local rotating black holes in higher dimension: geometry

With a help of a generalized Raychaudhuri equation non-expanding null surfaces are studied in arbitrarily dimensional case. The definition and basic properties of non-expanding and isolated horizons known in the literature in the 4 and 3 dimensional cases are generalized. A local description of horizon's geometry is provided. The Zeroth Law of black hole thermodynamics is derived. The constraints have a similar structure to that of the 4 dimensional spacetime case. The geometry of a vacuum isolated horizon is determined by the induced metric and the rotation 1-form potential, local generalizations of the area and the angular momentum typically used in the stationary black hole solutions case.Comment: 32 pages, RevTex