54195021
Casimir effect in the Hořava–Lifshitz gravity with a cosmological constant
Abstract We calculate the Casimir energy of a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed tangentially to the surface of a sphere with mass M and radius R . To this end, we take into account a static and spherically symmetric solution of Hořava–Lifshitz (HL) gravity, with a cosmological constant term, in lower orders of approximation, considering both weak-field and infrared limits. We show that the Casimir energy, just in the second order weak-field approximation, is modified due to the parameter of the HL gravity as well as to the cosmological constant.
13913247
N = 2 MAXWELL–CHERN–SIMONS MODEL WITH ANOMALOUS MAGNETIC MOMENT COUPLING VIA DIMENSIONAL REDUCTION
An N = 1-supersymmetric version of the Cremmer–Scherk–Kalb–Ramond model with nonminimal coupling to matter is built up both in terms of superfields and in a component-field formalism. By adopting a dimensional reduction procedure, the (N = 2)-(D = 3) counterpart of the model comes out, with two main features: a genuine (diagonal) Chern–Simons term and an anomalous magnetic moment coupling between matter and the gauge potential.
118935596
Hořava-Lifshitz gravity effects on Casimir energy in weak field approximation and infrared regime
We calculate the renormalized vacuum energy of a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed tangentially to the surface of a sphere with mass $M$ and radius $R$. This study will take into account the static and spherically symmetric solution of Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity found by Kehagias-Sfetsos (KS), in both weak field and infrared limits. A slight amplification of the Casimir force between the conducting plates is found. Thermal corrections to the Casimir energy are analyzed. Based on current Casimir effect measurements, a constraint on the $\ensuremath{\omega}$ parameter of KS metric is also obtained.
119663399
Analytic Results in the Position-Dependent Mass Schrödinger Problem
We investigate the Schrodinger equation for a particle with a nonuniform solitonic mass density. First, we discuss in extent the (nontrivial) position-dependent mass V(x) = 0 case whose solutions are hypergeometric functions in tanh2 x. Then, we consider an external hyperbolic-tangent potential. We show that the effective quantum mechanical problem is given by a Heun class equation and find analytically an eigenbasis for the space of solutions. We also compute the eigenstates for a potential of the form V(x) = V0 sinh2 x.
59387646
Theory of rapidly oscillating Ap stars
I review recent theoretical work on rapidly oscillating Ap stars and discuss key aspects of the physics of the oscillations observed in this class of pulsators.
118832639
On Solar Frequency Changes
The structure of the surface layers of the Sun is changed by magnetic activity which, in turn, changes the eigenfrequencies of the acoustic modes. These frequency shifts have been observed both in low- and high-degree data, and are found to be correlated with the solar cycle. Time-distance helioseismology has shown that waves travelling through sunspots suffer time delays. Also it is known that sunspots induce phase shifts between inwardly and outwardly propagating waves. In the present work we show how these phase shifts are related to the observed time delays by treating the scattering of acoustic waves off sunspots as a diffraction problem. These time delays are then related to the frequency shifts of the modes. From this relation we obtain a lower limit for the contribution of sunspots to the observed frequency variations with the solar cycle. Moreover, we predict the frequency dependence of the time delays suffered by rays travelling through a sunspot.
118382133
On the understanding of pulsations in the atmosphere of roAp stars: phase diversity and false nodes
Studies based on high-resolution spectroscopic data of rapidly oscillating Ap stars show a surprising diversity of pulsation behaviour in the atmospheric layers, pointing, in particular, to the co-existence of running and standing waves. The correct interpretation of these data requires a careful modelling of pulsations in these magnetic stars. In light of this, in this work we present a theoretical analysis of pulsations in roAp stars, taking into account the direct influence of the magnetic field. We derive approximate analytical solutions for the displacement components parallel and perpendicular to the direction of the magnetic field, that are appropriate to the outermost layer. From these, we determine the expression for the theoretical radial velocity for an observer at a general position, and compute the corresponding pulsation amplitude and phase as a function of height in the atmosphere. We show that the integral for the radial velocity has contributions from three different types of wave solutions, namely running waves, evanescent waves and standing waves of nearly constant amplitude. We then consider a number of case studies to illustrate the origin of the different pulsational behaviour that is found in the observations. Concerning pulsation amplitude, we find that it generally increases with atmospheric height. Pulsation phase, however, shows a diversity of behaviours, including phases that are constant, increasing or decreasing with atmospheric height. Finally, we show that there are situations in which the pulsation amplitude goes through a zero, accompanied by a phase jumps of π, and argue that such behaviour does not correspond to a pulsation node in the outermost layers of the star, but rather to a visual effect, resulting from the observers inability to resolve the stellar surface.
16795633
Theoretical aspects of roAp stars
The theoretical work on roAp stars is reviewed, especially in relation with observational facts that still need to be understood: high frequencies of the modes observed, which can be higher than the theoretical critical cutoff frequency for acoustic modes in these stars; their apparent alignment with the magnetic field, and the fact that some modes cannot be described by a single spherical harmonic.
119107445
Seismic signatures of stellar cores of solar‐like pulsators: Dependence on mass and age
Useful information from the inner layers of stellar pulsators may be derived from the study of their oscillations. In this paper we analyse three diagnostic tools suggested in the literature built from the oscillation frequencies computed for a set of main sequence models with masses between 1.0 M⊙ and 1.6 M⊙, to check what information they may hold about stellar cores. For the models with convective cores (M ≥ 1.2 M⊙) we find a relation between the frequency slopes of the diagnostic tools and the size of the jump in the sound speed at the edge of the core. We show that this relation is independent of the mass of the models. In practice, since the size of the jump in the sound speed is related to the age of the star, using these seismic tools we may, in principle, infer the star's evolutionary state. We also show that when combining two of the three diagnostic tools studied, we are able to distinguish models with convective cores from models without a convective core but with strong sound speed gradients in the inner layers (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)