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.+

Discussion quality diffuses in the digital public square

Studies of online social influence have demonstrated that friends have important effects on many types of behavior in a wide variety of settings. However, we know much less about how influence works among relative strangers in digital public squares, despite important conversations happening in such spaces. We present the results of a study on large public Facebook pages where we randomly used two different methods--most recent and social feedback--to order comments on posts. We find that the social feedback condition results in higher quality viewed comments and response comments. After measuring the average quality of comments written by users before the study, we find that social feedback has a positive effect on response quality for both low and high quality commenters. We draw on a theoretical framework of social norms to explain this empirical result. In order to examine the influence mechanism further, we measure the similarity between comments viewed and written during the study, finding that similarity increases for the highest quality contributors under the social feedback condition. This suggests that, in addition to norms, some individuals may respond with increased relevance to high-quality comments.Comment: 10 pages, 6 figures, 2 table

On a Petrov-type D homogeneous solution

We present a new two-parameter family of solutions of Einstein gravity with negative cosmological constant in 2+1 dimensions. These solutions are obtained by squashing the anti-de Sitter geometry along one direction and posses four Killing vectors. Global properties as well as the four dimensional generalization are discussed, followed by the investigation of the geodesic motion. A simple global embedding of these spaces as the intersection of four quadratic surfaces in a seven dimensional space is obtained. We argue also that these geometries describe the boundary of a four dimensional nutty-bubble solution and are relevant in the context of AdS/CFT correspondence.Comment: 20 pages, TeX fil

Space-Times Admitting Isolated Horizons

We characterize a general solution to the vacuum Einstein equations which admits isolated horizons. We show it is a non-linear superposition -- in precise sense -- of the Schwarzschild metric with a certain free data set propagating tangentially to the horizon. This proves Ashtekar's conjecture about the structure of spacetime near the isolated horizon. The same superposition method applied to the Kerr metric gives another class of vacuum solutions admitting isolated horizons. More generally, a vacuum spacetime admitting any null, non expanding, shear free surface is characterized. The results are applied to show that, generically, the non-rotating isolated horizon does not admit a Killing vector field and a spacetime is not spherically symmetric near a symmetric horizon.Comment: 11 pages, no figure

Probing semiclassical magneto-oscillations in the low-field quantum Hall effect

The low-field quantum Hall effect is investigated on a two-dimensional electron system in an AlGaAs/GaAs heterostructure. Magneto-oscillations following the semiclassical Shubnikov-de Haas formula are observed even when the emergence of the mobility gap shows the importance of quantum localization effects. Moreover, the Lifshitz-Kosevich formula can survive as the oscillating amplitude becomes large enough for the deviation to the Dingle factor. The crossover from the semiclassical transport to the description of quantum diffusion is discussed. From our study, the difference between the mobility and cyclotron gaps indicates that some electron states away from the Landau-band tails can be responsible for the semiclassical behaviors under low-field Landau quantization.Comment: 14 pages, 6 figure

Geometrical properties of the trans-spherical solutions in higher dimensions

We investigate the geometrical properties of static vacuum $p$-brane solutions of Einstein gravity in $D=n+p+3$ dimensions, which have spherical symmetry of $S^{n+1}$ orthogonal to the $p$-directions and are invariant under the translation along them. % The solutions are characterized by mass density and $p$ tension densities. % The causal structure of the higher dimensional solutions is essentially the same as that of the five dimensional ones. Namely, a naked singularity appears for most solutions except for the Schwarzschild black $p$-brane and the Kaluza-Klein bubble. % We show that some important geometric properties such as the area of $S^{n+1}$ and the total spatial volume are characterized only by the three parameters such as the mass density, the sum of tension densities and the sum of tension density squares rather than individual tension densities. These geometric properties are analyzed in detail in this parameter space and are compared with those of 5-dimensional case.Comment: 14 pages, 2 figures, Title change

Some Physical Consequences of Abrupt Changes in the Multipole Moments of a Gravitating Body

The Barrab\`es-Israel theory of light-like shells in General Relativity is used to show explicitly that in general a light-like shell is accompanied by an impulsive gravitational wave. The gravitational wave is identified by its Petrov Type N contribution to a Dirac delta-function term in the Weyl conformal curvature tensor (with the delta-function singular on the null hypersurface history of the wave and shell). An example is described in which an asymptotically flat static vacuum Weyl space-time experiences a sudden change across a null hypersurface in the multipole moments of its isolated axially symmetric source. A light-like shell and an impulsive gravitational wave are identified, both having the null hypersurface as history. The stress-energy in the shell is dominated (at large distance from the source) by the jump in the monopole moment (the mass) of the source with the jump in the quadrupole moment mainly responsible for the stress being anisotropic. The gravitational wave owes its existence principally to the jump in the quadrupole moment of the source confirming what would be expected.Comment: 26 pages, tex, no figures, to appear in Phys.Rev.

Anomalous scattering of highly dispersed pulsars

We report multifrequency measurements of scatter broadening times for nine highly dispersed pulsars over a wide frequency range (0.6 -- 4.9 GHz). We find the scatter broadening times to be larger than expected and to scale with frequency with an average power-law index of $3.44\pm 0.13$, i.e. significantly less than that expected from standard theories. Such possible discrepancies have been predicted very recently by Cordes & Lazio.Comment: 7 pages, 4 figures, accepted for publication in ApJ Letter

Information Content in B→VVB \to VV Decays and the Angular Moments Method

The time-dependent angular distributions of decays of neutral $B$ mesons into two vector mesons contain information about the lifetimes, mass differences, strong and weak phases, form factors, and CP violating quantities. A statistical analysis of the information content is performed by giving the ``information'' a quantitative meaning. It is shown that for some parameters of interest, the information content in time and angular measurements combined may be orders of magnitude more than the information from time measurements alone and hence the angular measurements are highly recommended. The method of angular moments is compared with the (maximum) likelihood method to find that it works almost as well in the region of interest for the one-angle distribution. For the complete three-angle distribution, an estimate of possible statistical errors expected on the observables of interest is obtained. It indicates that the three-angle distribution, unraveled by the method of angular moments, would be able to nail down many quantities of interest and will help in pointing unambiguously to new physics.Comment: LaTeX, 34 pages with 9 figure