Zeta-function approach to Casimir energy with singular potentials

In the framework of zeta-function approach the Casimir energy for three simple model system: single delta potential, step function potential and three delta potentials is analyzed. It is shown that the energy contains contributions which are peculiar to the potentials. It is suggested to renormalize the energy using the condition that the energy of infinitely separated potentials is zero which corresponds to subtraction all terms of asymptotic expansion of zeta-function. The energy obtained in this way obeys all physically reasonable conditions. It is finite in the Dirichlet limit and it may be attractive or repulsive depending on the strength of potential. The effective action is calculated and it is shown that the surface contribution appears. The renormalization of the effective action is discussed.Comment: 17 pages, 2 figures, added reference, address correcte

Self-force of a point charge in the space-time of a symmetric wormhole

We consider the self-energy and the self-force for an electrically charged particle at rest in the wormhole space-time. We develop general approach and apply it to two specific profiles of the wormhole throat with singular and with smooth curvature. The self-force for these two profiles is found in manifest form; it is an attractive force. We also find an expression for the self-force in the case of arbitrary symmetric throat profile. Far from the throat the self-force is always attractive.Comment: 18 pages, 3 figures Comments: corrected pdf, enlarged pape

On the Spatial Distribution of Stellar Populations in the Large Magellanic Cloud

We measure the angular correlation function of stars in a region of the Large Magellanic Cloud (LMC) that spans 2 degrees by 1.5 degrees. We find that the correlation functions of stellar populations are represented well by exponential functions of the angular separation for separations between 2 and 40 arcmin (corresponding to ~ 30 pc and 550 pc for an LMC distance of 50 kpc). The inner boundary is set by the presence of distinct, highly correlated structures, which are the more familiar stellar clusters, and the outer boundary is set by the observed region's size and the presence of two principal centers of star formation within the region. We also find that the normalization and scale length of the correlation function changes systematically with the mean age of the stellar population. The existence of positive correlation at large separations (~300 pc), even in the youngest population, argues for large-scale hierarchical structure in current star formation. The evolution of the angular correlation toward lower normalizations and longer scale lengths with stellar age argues for the dispersion of stars with time. We show that a simple, stochastic, self-propagating star formation model is qualitatively consistent with this behavior of the correlation function.Comment: 30 pages, 13 Figures. Scheduled for publication in AJ in June 199

Casimir effect in a wormhole spacetime

We consider the Casimir effect for quantized massive scalar field with non-conformal coupling $\xi$ in a spacetime of wormhole whose throat is rounded by a spherical shell. In the framework of zeta-regularization approach we calculate a zero point energy of scalar field. We found that depending on values of coupling $\xi$, a mass of field $m$, and/or the throat's radius $a$ the Casimir force may be both attractive and repulsive, and even equals to zero.Comment: 2 figures, 10 pages, added 2 reference

Ground state energy in a wormhole space-time

The ground state energy of the massive scalar field with non-conformal coupling $\xi$ on the short-throat flat-space wormhole background is calculated by using zeta renormalization approach. We discuss the renormalization and relevant heat kernel coefficients in detail. We show that the stable configuration of wormholes can exist for $\xi > 0.123$. In particular case of massive conformal scalar field with $\xi=1/6$, the radius of throat of stable wormhole $a\approx 0.16/m$. The self-consistent wormhole has radius of throat $a\approx 0.0141 l_p$ and mass of scalar boson $m\approx 11.35 m_p$ ($l_p$ and $m_p$ are the Planck length and mass, respectively).Comment: revtex, 18 pages, 3 eps figures. accepted in Phys.Rev.

HV 11423: The Coolest Supergiant in the SMC

We call attention to the fact that one of the brightest red supergiants in the SMC has recently changed its spectral type from K0-1 I (December 2004) to M4 I (December 2005) and back to K0-1 I (September 2006). An archival spectrum from the Very Large Telescope reveals that the star was even cooler (M4.5-M5 I) in December 2001. By contrast, the star was observed to be an M0 I in both October 1978 and October 1979. The M4-5 I spectral types is by far the latest type seen for an SMC supergiant, and its temperature in that state places it well beyond the Hayashi limit into a region of the H-R diagram where the star should not be in hydrostatic equilibrium. The star is variable by nearly 2 mag in V, but essentially constant in K. Our modeling of its spectral energy distribution shows that the visual extinction has varied during this time, but that the star has remained essentially constant in bolometric luminosity. We suggest that the star is currently undergoing a period of intense instability, with its effective temperature changing from 4300 K to 3300 K on the time-scale of months. It has one of the highest 12-micron fluxes of any RSG in the SMC, and we suggest that the variability at V is due primarily to changes in effective temperature, and secondly, due to changes in the local extinction due to creation and dissipation of circumstellar dust. We speculate that the star may be nearing the end of its life.Comment: Accepted by the Astrophysical Journa

Vacuum Expectation Value of the Spinor Massive field in the Cosmic String Space-Time

We found the contribution to the vacuum expectation value of the energy-momentum tensor of a massive Dirac field due to the conical geometry of the cosmic string space-time. The heat kernel and heat kernel expansion for the squared Dirac operator in this background are also considered and the first three coefficients were found in an explicity form.Comment: 9 pages, 1 figure (2 ref added) (enlarged version

Group classification of the Sachs equations for a radiating axisymmetric, non-rotating, vacuum space-time

We carry out a Lie group analysis of the Sachs equations for a time-dependent axisymmetric non-rotating space-time in which the Ricci tensor vanishes. These equations, which are the first two members of the set of Newman-Penrose equations, define the characteristic initial-value problem for the space-time. We find a particular form for the initial data such that these equations admit a Lie symmetry, and so defines a geometrically special class of such spacetimes. These should additionally be of particular physical interest because of this special geometric feature.Comment: 18 Pages. Submitted to Classical and Quantum Gravit

Soliton Interactions in Perturbed Nonlinear Schroedinger Equations

We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schroedinger equation under the influence of a small correction to the nonlinear potential. We assume that the solitons are all moving with the same velocity at the initial instant; this maximizes the effect each soliton has on the others as a consequence of the perturbation. Over the long time scales that we consider, the amplitudes of the solitons remain fixed, while their center of mass coordinates obey Newton's equations with a force law for which we present an integral formula. For the interaction of two solitons with a quintic perturbation term we present more details since symmetries -- one related to the form of the perturbation and one related to the small number of particles involved -- allow the problem to be reduced to a one-dimensional one with a single parameter, an effective mass. The main results include calculations of the binding energy and oscillation frequency of nearby solitons in the stable case when the perturbation is an attractive correction to the potential and of the asymptotic "ejection" velocity in the unstable case. Numerical experiments illustrate the accuracy of the perturbative calculations and indicate their range of validity.Comment: 28 pages, 7 figures, Submitted to Phys Rev E Revised: 21 pages, 6 figures, To appear in Phys Rev E (many displayed equations moved inline to shorten manuscript