Resolving Gamma-Ray Burst 000301C with a Gravitational Microlens

The afterglow of the Gamma-Ray Burst (GRB) 000301C exhibited achromatic, short time-scale variability that is difficult to reconcile with the standard relativistic shock model. We interpret the observed light curves as a microlensing event superimposed on power-law flux decays typical of afterglows. In general, a relativistic GRB shock appears on the sky as a thin ring expanding at a superluminal speed. Initially the ring is small relative to its angular separation from the lens and so its flux is magnified by a constant factor. As the ring grows and sweeps across the lens its magnification reaches a maximum. Subsequently, the flux gradually recovers its unlensed value. This behavior involves only three free parameters in its simplest formulation and was predicted theoretically by Loeb & Perna (1998). Fitting the available R-band photometric data of GRB 000301C to a simple model of the microlensing event and a broken power-law for the afterglow, we find reasonable values for all the parameters and a reduced chi^2/DOF parameter of 1.48 compared with 2.99 for the broken power-law fit alone. The peak magnification of ~2 occurred 3.8 days after the burst. The entire optical-IR data imply a width of the GRB ring of order 10% of its radius, similar to theoretical expectations. The angular resolution provided by microlensing is better than a micro-arcsecond. We infer a mass of approximately 0.5 M_Sun for a lens located half way to the source at z_s=2.04. A galaxy 2'' from GRB 000301C might be the host of the stellar lens, but current data provides only an upper-limit on its surface brightness at the GRB position.Comment: to appear in the ApJ Letters, 13 pages, 3 figures (one additional figure included); all data used for the fits available at ftp://cfa-ftp.harvard.edu/pub/kstanek/GRB000301C/ and through WWW at http://cfa-www.harvard.edu/cfa/oir/Research/GRB

Cylindrically symmetric wormholes

This paper discusses traversable wormholes that differ slightly but significantly from those of the Morris-Thorne type under the assumption of cylindrical symmetry. The throat is a piecewise smooth cylindrical surface resulting in a shape function that is not differentiable at some value. It is proposed that the regular derivative be replaced by a one-sided derivative at this value. The resulting wormhole geometry satisfies the weak energy condition.Comment: Supplied missing figures; 15 pages AMSTe

Maximum Mass-Radius Ratio for Compact General Relativistic Objects in Schwarzschild- de Sitter Geometry

Upper limits for the mass-radius ratio are derived for arbitrary general relativistic matter distributions in the presence of a cosmological constant. General restrictions for the red shift and total energy (including the gravitational contribution) for compact objects in the Schwarzschild-de Sitter geometry are also obtained in terms of the cosmological constant and of the mean density of the star.Comment: 8 pages, no figure

A detailed analysis of structure growth in f(R)f(R) theories of gravity

We investigate the connection between dark energy and fourth order gravity by analyzing the behavior of scalar perturbations around a Friedmann-Robertson-Walker background. The evolution equations for scalar perturbation are derived using the covariant and gauge invariant approach and applied to two widely studied $f(R)$ gravity models. The structure of the general fourth order perturbation equations and the analysis of scalar perturbations lead to the discovery of a characteristic signature of fourth order gravity in the matter power spectrum, the details of which have not seen before in other works in this area. This could provide a crucial test for fourth order gravity on cosmological scales.Comment: 27 pages and 35 figure

Symplectic SUSY Gauge Theories with Antisymmetric Matter

We investigate the confining phase vacua of supersymmetric Sp(2\NC) gauge theories that contain matter in both fundamental and antisymmetric representations. The moduli spaces of such models with \NF=3 quark flavors and \NA=1 antisymmetric field are analogous to that of SUSY QCD with \NF=\NC+1 flavors. In particular, the forms of their quantum superpotentials are fixed by classical constraints. When mass terms are coupled to W_{(\NF=3,\NA=1)} and heavy fields are integrated out, complete towers of dynamically generated superpotentials for low energy theories with fewer numbers of matter fields can be derived. Following this approach, we deduce exact superpotentials in $Sp(4)$ and $Sp(6)$ theories which cannot be determined by symmetry considerations or integrating in techniques. Building upon these simple symplectic group results, we also examine the ground state structures of several $Sp(4) \times Sp(4)$ and $Sp(6) \times Sp(2)$ models. We emphasize that the top-down approach may be used to methodically find dynamical superpotentials in many other confining supersymmetric gauge theories.Comment: 21 pages, Revte

Statistics of work performed on a forced quantum oscillator

Various aspects of the statistics of work performed by an external classical force on a quantum mechanical system are elucidated for a driven harmonic oscillator. In this special case two parameters are introduced that are sufficient to completely characterize the force protocol. Explicit results for the characteristic function of work and the respective probability distribution are provided and discussed for three different types of initial states of the oscillator: microcanonical, canonical and coherent states. Depending on the choice of the initial state the probability distributions of the performed work may grossly differ. This result in particular holds also true for identical force protocols. General fluctuation and work theorems holding for microcanonical and canonical initial states are confirmed

Honey bee colony losses

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