33,652 research outputs found

    An explanation of the Newman-Janis Algorithm

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    After the original discovery of the Kerr metric, Newman and Janis showed that this solution could be ``derived'' by making an elementary complex transformation to the Schwarzschild solution. The same method was then used to obtain a new stationary axisymmetric solution to Einstein's field equations now known as the Kerr-newman metric, representing a rotating massive charged black hole. However no clear reason has ever been given as to why the Newman-Janis algorithm works, many physicist considering it to be an ad hoc procedure or ``fluke'' and not worthy of further investigation. Contrary to this belief this paper shows why the Newman-Janis algorithm is successful in obtaining the Kerr-Newman metric by removing some of the ambiguities present in the original derivation. Finally we show that the only perfect fluid generated by the Newman-Janis algorithm is the (vacuum) Kerr metric and that the only Petrov typed D solution to the Einstein-Maxwell equations is the Kerr-Newman metric.Comment: 14 pages, no figures, submitted to Class. Quantum Gra

    Identity and Search in Social Networks

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    Social networks have the surprising property of being "searchable": Ordinary people are capable of directing messages through their network of acquaintances to reach a specific but distant target person in only a few steps. We present a model that offers an explanation of social network searchability in terms of recognizable personal identities: sets of characteristics measured along a number of social dimensions. Our model defines a class of searchable networks and a method for searching them that may be applicable to many network search problems, including the location of data files in peer-to-peer networks, pages on the World Wide Web, and information in distributed databases.Comment: 4 page, 3 figures, revte

    Deep Inelastic Lepton-Nucleon Scattering at HERA

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    Data from the HERA collider experiments, H1 and ZEUS, have been fundamental to the rapid recent development of our understanding of the partonic composition of the proton and of QCD. This report focuses on inclusive measurements of neutral and charged current cross sections at HERA, using the full available data taken to date. The present precision on the proton parton densities and the further requirements for future measurements at the Tevatron and LHC are explored. Emphasis is also placed on the region of very low Bjorken-x and Q^2. In this region, the `confinement' transition takes place from partons to hadrons as the relevant degrees of freedom and novel or exotic QCD effects associated with large parton densities are most likely to be observed. Finally, prospects for the second phase of HERA running are discussed.Comment: 13 pages, 15 figures, to appear in Proceedings of the XXI International Symposium on lepton and Photon Interactions at High Energies, Fermilab, August 200

    Sign-time distributions for interface growth

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    We apply the recently introduced distribution of sign-times (DST) to non-equilibrium interface growth dynamics. We are able to treat within a unified picture the persistence properties of a large class of relaxational and noisy linear growth processes, and prove the existence of a non-trivial scaling relation. A new critical dimension is found, relating to the persistence properties of these systems. We also illustrate, by means of numerical simulations, the different types of DST to be expected in both linear and non-linear growth mechanisms.Comment: 4 pages, 5 ps figs, replaced misprint in authors nam

    MOSFIRE Absorption Line Spectroscopy of z > 2 Quiescent Galaxies: Probing a Period of Rapid Size Growth

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    Using the MOSFIRE near-infrared multi-slit spectrograph on the Keck 1 Telescope, we have secured high signal-to-noise ratio absorption line spectra for six massive galaxies with redshift 2 < z < 2.5. Five of these galaxies lie on the red sequence and show signatures of passive stellar populations in their rest-frame optical spectra. By fitting broadened spectral templates we have determined stellar velocity dispersions and, with broad-band HST and Spitzer photometry and imaging, stellar masses and effective radii. Using this enlarged sample of galaxies we confirm earlier suggestions that quiescent galaxies at z > 2 have small sizes and large velocity dispersions compared to local galaxies of similar stellar mass. The dynamical masses are in very good agreement with stellar masses (log Mstar/Mdyn = -0.02 +/- 0.03), although the average stellar-to-dynamical mass ratio is larger than that found at lower redshift (-0.23 +/- 0.05). By assuming evolution at fixed velocity dispersion, not only do we confirm a surprisingly rapid rate of size growth but we also consider the necessary evolutionary track on the mass-size plane and find a slope alpha = dlogR / dlogM > ~2 inconsistent with most numerical simulations of minor mergers. Both results suggest an additional mechanism may be required to explain the size growth of early galaxies.Comment: Updated to match the published versio

    A Cosmic Variance Cookbook

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    Deep pencil beam surveys (<1 deg^2) are of fundamental importance for studying the high-redshift universe. However, inferences about galaxy population properties are in practice limited by 'cosmic variance'. This is the uncertainty in observational estimates of the number density of galaxies arising from the underlying large-scale density fluctuations. This source of uncertainty can be significant, especially for surveys which cover only small areas and for massive high-redshift galaxies. Cosmic variance for a given galaxy population can be determined using predictions from cold dark matter theory and the galaxy bias. In this paper we provide tools for experiment design and interpretation. For a given survey geometry we present the cosmic variance of dark matter as a function of mean redshift z and redshift bin size Dz. Using a halo occupation model to predict galaxy clustering, we derive the galaxy bias as a function of mean redshift for galaxy samples of a given stellar mass range. In the linear regime, the cosmic variance of these galaxy samples is the product of the galaxy bias and the dark matter cosmic variance. We present a simple recipe using a fitting function to compute cosmic variance as a function of the angular dimensions of the field, z, Dz and stellar mass m*. We also provide tabulated values and a software tool. We find that for GOODS at z=2 and with Dz=0.5 the relative cosmic variance of galaxies with m*>10^11 Msun is ~38%, while it is ~27% for GEMS and ~12% for COSMOS. For galaxies of m*~10^10 Msun the relative cosmic variance is ~19% for GOODS, ~13% for GEMS and ~6% for COSMOS. This implies that cosmic variance is a significant source of uncertainty at z=2 for small fields and massive galaxies, while for larger fields and intermediate mass galaxies cosmic variance is less serious.Comment: 8 pages, 4 figures, 5 tables, submitted to Ap

    Scale-freeness for networks as a degenerate ground state: A Hamiltonian formulation

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    The origin of scale-free degree distributions in the context of networks is addressed through an analogous non-network model in which the node degree corresponds to the number of balls in a box and the rewiring of links to balls moving between the boxes. A statistical mechanical formulation is presented and the corresponding Hamiltonian is derived. The energy, the entropy, as well as the degree distribution and its fluctuations are investigated at various temperatures. The scale-free distribution is shown to correspond to the degenerate ground state, which has small fluctuations in the degree distribution and yet a large entropy. We suggest an implication of our results from the viewpoint of the stability in evolution of networks.Comment: 7 pages, 3 figures. To appear in Europhysics lette
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