Non-Quasinormal Modes and Black Hole Physics

The near-horizon geometry of a large class of extremal and near-extremal black holes in string and M theory contains three-dimensional asymptotically anti-de Sitter space. Motivated by this structure, we are led naturally to a discrete set of complex frequencies defined in terms of the monodromy at the inner and outer horizons of the black hole. We show that the correspondence principle, whereby the real part of these ``non-quasinormal frequencies'' is identified with certain fundamental quanta, leads directly to the correct quantum behavior of the near-horizon Virasoro algebra, and thus the black hole entropy. Remarkably, for the rotating black hole in five dimensions we also reproduce the fractionization of conformal weights predicted in string theory.Comment: 4 pages, revtex4; v2: reference added; v3: more references, minor typo corrected; v4: minor rewording to adjust size (ugh!); v5: some small clarifications at referees' suggestio

Observations of electron gyroharmonic waves and the structure of the Io torus

Narrow-banded emissions were observed by the Planetary Radio Astronomy experiment on the Voyager 1 spacecraft as it traversed the Io plasma torus. These waves occur between harmonics of the electron gyrofrequency and are the Jovian analogue of electrostatic emissions observed and theoretically studied for the terrestrial magnetosphere. The observed frequencies always include the component near the upper hybrid resonant frequency, (fuhr) but the distribution of the other observed emissions varies in a systematic way with position in the torus. A refined model of the electron density variation, based on identification of the fuhr line, is included. Spectra of the observed waves are analyzed in terms of the linear instability of an electron distribution function consisting of isotropic cold electrons and hot losscone electrons. The positioning of the observed auxiliary harmonics with respect to fuhr is shown to be an indicator of the cold to hot temperature ratio. It is concluded that this ratio increases systematically by an overall factor of perhaps 4 or 5 between the inner and outer portions of the torus

Topological Modes in Dual Lattice Models

Lattice gauge theory with gauge group $Z_{P}$ is reconsidered in four dimensions on a simplicial complex $K$. One finds that the dual theory, formulated on the dual block complex $\hat{K}$, contains topological modes which are in correspondence with the cohomology group $H^{2}(\hat{K},Z_{P})$, in addition to the usual dynamical link variables. This is a general phenomenon in all models with single plaquette based actions; the action of the dual theory becomes twisted with a field representing the above cohomology class. A similar observation is made about the dual version of the three dimensional Ising model. The importance of distinct topological sectors is confirmed numerically in the two dimensional Ising model where they are parameterized by $H^{1}(\hat{K},Z_{2})$.Comment: 10 pages, DIAS 94-3

An Exact Black Hole Entropy Bound

We show that a Rademacher expansion can be used to establish an exact bound for the entropy of black holes within a conformal field theory framework. This convergent expansion includes all subleading corrections to the Bekenstein-Hawking term.Comment: 6 pages, Latex, v2 minor re-wording, additional reference, to appear in Phyical Review D (title changed in journal

A Closed Contour of Integration in Regge Calculus

The analytic structure of the Regge action on a cone in $d$ dimensions over a boundary of arbitrary topology is determined in simplicial minisuperspace. The minisuperspace is defined by the assignment of a single internal edge length to all 1-simplices emanating from the cone vertex, and a single boundary edge length to all 1-simplices lying on the boundary. The Regge action is analyzed in the space of complex edge lengths, and it is shown that there are three finite branch points in this complex plane. A closed contour of integration encircling the branch points is shown to yield a convergent real wave function. This closed contour can be deformed to a steepest descent contour for all sizes of the bounding universe. In general, the contour yields an oscillating wave function for universes of size greater than a critical value which depends on the topology of the bounding universe. For values less than the critical value the wave function exhibits exponential behaviour. It is shown that the critical value is positive for spherical topology in arbitrary dimensions. In three dimensions we compute the critical value for a boundary universe of arbitrary genus, while in four and five dimensions we study examples of product manifolds and connected sums.Comment: 16 pages, Latex, To appear in Gen. Rel. Gra

Social interactions through the eyes of macaques and humans

Group-living primates frequently interact with each other to maintain social bonds as well as to compete for valuable resources. Observing such social interactions between group members provides individuals with essential information (e.g. on the fighting ability or altruistic attitude of group companions) to guide their social tactics and choice of social partners. This process requires individuals to selectively attend to the most informative content within a social scene. It is unclear how non-human primates allocate attention to social interactions in different contexts, and whether they share similar patterns of social attention to humans. Here we compared the gaze behaviour of rhesus macaques and humans when free-viewing the same set of naturalistic images. The images contained positive or negative social interactions between two conspecifics of different phylogenetic distance from the observer; i.e. affiliation or aggression exchanged by two humans, rhesus macaques, Barbary macaques, baboons or lions. Monkeys directed a variable amount of gaze at the two conspecific individuals in the images according to their roles in the interaction (i.e. giver or receiver of affiliation/aggression). Their gaze distribution to non-conspecific individuals was systematically varied according to the viewed species and the nature of interactions, suggesting a contribution of both prior experience and innate bias in guiding social attention. Furthermore, the monkeys’ gaze behavior was qualitatively similar to that of humans, especially when viewing negative interactions. Detailed analysis revealed that both species directed more gaze at the face than the body region when inspecting individuals, and attended more to the body region in negative than in positive social interactions. Our study suggests that monkeys and humans share a similar pattern of role-sensitive, species- and context-dependent social attention, implying a homologous cognitive mechanism of social attention between rhesus macaques and humans