Massive scalar field quasinormal modes of a black hole with quintessence-like matter and a deficit solid angle

Using the third-order WKB approximation, we evaluate the quasinormal frequencies of massive scalar field perturbation around a black hole with quintessence-like matter and a deficit solid angle. The mass u of the scalar field plays an important role in studying the quasinormal frequencies. We find that as the scalar field mass increases when the other parameters are fixed, so do the real parts and the magnitudes of the imaginary parts of the quasinormal frequencies decrease. The imaginary parts are almost linearly related to the real parts.     

A simple derivation of level spacing of quasinormal frequencies for a black hole with a deficit solid angle and quintessence-like matter

In this paper, we investigate analytically the level space of the imaginary part of quasinormal frequencies for a black hole with a deficit solid angle and quintessence-like matter by the Padmanabhan’s method (Padmanabhan in Class. Quantum Gravity 21:L1, 2004). Padmanabhan presented a method to study analytically the imaginary part of quasinormal frequencies for a class of spherically symmetric spacetimes including Schwarzschild-de Sitter black holes which has an evenly spaced structure. The results show that the level space of scalar and gravitational quasinormal frequencies for this kind of black holes only depend on the surface gravity of black-hole horizon in the range of $-1<w<-\frac{1}{3}$ , respectively. We also extend the range of w to w≤?1, the results of which are similar to that in $-1<w<-\frac{1}{3}$ case. Particularly, a black hole with a deficit solid angle in accelerating universe will be a Schwarzschild-de Sitter black hole, fixing w=?1 and ε ²=0. And a black hole with a deficit solid angle in the accelerating universe will be a Schwarzschild black hole,when ρ ₀=0 and ε ²=0. In this paper, w is the parameter of state equation, ε ² is a parameter relating to a deficit solid angle and ρ ₀ is the density of static spherically symmetrical quintessence-like matter at r=1.     

Quasinormal modes of scalar perturbation around a quantum-corrected Schwarzschild black hole

In this paper, we evaluate quasinormal modes (QNMs) of scalar perturbations around a quantum-corrected Schwarzschild black hole by using the third order Wentzel-Kramers-Brillouin (WKB) approximation method. The results show that due to the quantum fluctuations in the background of the Schwarzschild black hole, the QNMs of the black hole damp more slowly when increasing the quantum correction factor (a), and oscillate more slowly.     

Quasinormal modes of a black hole with quintessence-like matter and a deficit solid angle: scalar and gravitational perturbations

In the previous paper (Li et al. in Phys. Lett. B 666:125–130, 2008), we show the solutions of Einstein equations with static spherically-symmetric quintessence-like matter surrounding a global monopole. Furthermore, this monopole become a black hole with quintessence-like matter and a deficit solid angle when it is swallowed by an ordinary black hole. We study its quasinormal modes by WKB method in this paper. The numerical results show that both the real part of the quasinormal frequencies and the imaginary part decrease as the state parameter w, for scalar and gravitational perturbations. And we also show variations of quasinormal frequencies of scalar and gravitational fields via different ε (deficit solid angel parameter) and different ρ ₀ (density of static spherically-symmetric quintessence-like matter at r=1), respectively.     

Dirac quasinormal modes of a black hole with quintessence-like matter and a deficit solid angle

Using the third-order WKB approximation, we evaluate the quasinormal frequencies of massless Dirac field perturbation around a black hole with quintessence-like matter and a deficit solid angle. We discuss carefully the properties of quasinormal frequencies with the change of quintessential state parameter w _q , the deficit solid angle parameter ε, the energy density of quintessence-like matter ρ ₀, and the total angular momentum number |k| and the overtone number n, respectively.     

Dirac quasinormal modes of the deformed Hořava-Lifshitz black hole spacetime

Using the third-order WKB approximation, we evaluate the quasinormal frequencies of massless Dirac field perturbation around a deformed black hole in the Hořava-Lifshitz gravity with coupling constant λ=1. Our result shows that the Hořava-Lifshitz parameter α plays an important role for the quasinormal frequencies and we discuss the variation of quasinormal frequencies with α. Moreover, we find that the massless Dirac field perturbations decay more slowly in the deformed Hořava-Lifshitz gravity.     

Dark Matter from the inflaton field

We present a model where inflation and Dark Matter takes place via a single scalar field ?. Without introducing any new parameters we are able unify inflation and Dark Matter using a scalar field ? that accounts for inflation at an early epoch while it gives a Dark Matter WIMP particle at low energies. After inflation our universe must be reheated and we must have a long period of radiation dominated before the epoch of Dark Matter. Typically the inflaton decays while it oscillates around the minimum of its potential. If the inflaton decay is not complete or sufficient then the remaining energy density of the inflaton after reheating must be fine tuned to give the correct amount of Dark Matter. An essential feature here, is that Dark Matter-Inflaton particle is produced at low energies without fine tuning or new parameters. This process uses the same coupling g as for the inflaton decay. Once the field ? becomes non-relativistic it will decouple as any WIMP particle, since n_? is exponentially suppressed. The correct amount of Dark Matter determines the cross section and we have a constraint between the coupling g and the mass m_o of ?. The unification scheme we present here has four free parameters, two for the scalar potential V(?) given by the inflation parameter λ of the quartic term and the mass m_o. The other two parameters are the coupling g between the inflaton ? and a scalar filed φ and the coupling h between φ with standard model particles ψ or χ. These four parameters are already present in models of inflation and reheating process, without considering Dark Matter. Therefore, our unification scheme does not increase the number of parameters and it accomplishes the desired unification between the inflaton and Dark Matter for free.     

Scalar field power-law cosmology with spatial curvature and dark energy-dark matter interaction

We consider a late closed universe of which scale factor is a power function of time using observational data from combined WMAP5+BAO+SN Ia dataset and WMAP5 dataset. The WMAP5 data give power-law exponent, α=1.01 agreeing with the previous study of H(z) data while combined data gives α=0.985. Considering a scalar field dark energy and dust fluid evolving in the power-law universe, we find field potential, field solution and equation of state parameters. Decaying from dark matter into dark energy is allowed in addition to the non-interaction case. Time scale characterizing domination of the kinematic expansion terms over the dust and curvature terms in the scalar field potential are found to be approximately 5.3 to 5.5 Gyr. The interaction affects in slightly lowering the height of scalar potential and slightly shifting potential curves rightwards to later time. Mass potential function of the interacting Lagrangian term is found to be exponentially decay function.     

Diffussion of a scalar field in a compressible turbulent medium

The diffusion of scalar fields (temperature, density number of some admixture) in a compressible medium showing an isotropic, homogeneous and stationary turbulence is considered. The derived formulae for turbulent diffusivity χ_T(ξ) hold up to ξ ≈ 1, where ξ = u₀ τ₀/R₀ (u₀, τ₀, and R₀ are characteristic velocity, life-time, and correlation length of turbulent pulsations, respectively. The velocity field of turbulent motions u(r, t) is assumed to be known and the influence of the scalar field onto u(r, t) is neglected. It is shown that the velocity correlators, which change their signs in dependence on the space corrdinates, may give negative values for ξ_T(ξ) when ξ ≠ 0.     

Rotational perturbations of charged cosmological viscous-fluid universes coupled with a scalar field

The dynamics of a slowly rotating charged viscous-fluid Universe coupled with a zero-mass scalar field is investigated; and the rotational perturbations of such models are studied in order to substantiate the possibility that the Universe is endowed with slow rotation, in the course of presentation of several new analytic solutions. The effects of charged field and scalar field on the rotational motion are discussed. Except for perfect dragging, the scalar field as well as the charged field is found to have a damping effect on the rotation of matter. Rotating models which are expanding as well are obtained, in which cases the rotational velocities are found to decay with the time, and these models may be taken as good examples of real astrophysical situations. The periods of physical validity of different models are also obtained.     

Simulation of f-Mode Propagation Through a Cluster of Small Identical Magnetic Flux Tubes

Motivated by the question of how to distinguish seismically between monolithic and cluster models of sunspots, we have simulated the propagation of an f-mode wave packet through two identical small magnetic flux tubes (R=200 km), embedded in a stratified atmosphere. We want to study the effect of separation d and incidence angle χ on the scattered wave. We have demonstrated that the horizontal compact pair of tubes (d/R=2, χ=0) oscillate as a single tube when the incident wave is propagating, which gives a scattered wave amplitude of about twice that from a single tube. The scattered amplitude decreases with increasing d when d is about λ/2π where λ is the wavelength of the incident wave packet. In this case the individual tubes start to oscillate separately in the manner of near-field scattering. When d is about twice λ/2π, scattering from individual tubes reaches the far-field regime, giving rise to coherent scattering with an amplitude similar to the case of the compact pair of tubes. For perpendicular incidence (χ=π/2), the tubes oscillate simultaneously with the incident wave packet. Moreover, simulations show that a compact cluster oscillates almost as a single individual small tube and acts more like a scattering object, while a loose cluster shows multiple-scattering in the near field and the absorption is largest when d within the cluster is about λ/2π. This is the first step to understand the seismic response of a bundle of magnetic flux tubes in the context of sunspot and plage helioseismology.     

Spatial and temporal structure of a high-latitude transient ULF pulsation

Auroral radar observations of transient ULF pulsations with latitudinally varying period have recently been reported. An event of this type is analysed using data from the Scandinavian Magnetometer Array, the STARE radar, and the GEOS-2 satellite. The magnetometers show long-period (～450 s) oscillations consistent with the pulsations observed in the ionosphere using STARE, and confirm that the geomagnetic field shells are resonating in the toroidal mode. There is also a localised, small-amplitude component with 250-s period South of the STARE pulsations. Electric field measurements at GEOS-2 show only an impulsively stimulated pulsation of 250-s period. The wave fields at GEOS-2 imply that the satellite was earthward of a localised toroidal standing-wave resonance, which mapped to the ionosphere at least one degree South of the expected position. A radial profile of equatorial plasma mass density is inferred from the GEOS-2 and STARE results. This shows a radially increasing density near GEOS-2, and a radially decreasing density outside the satellite position.An interpretation of the event is given in which a tailward propagating hydromagnetic impulse directly stimulates field shells outside 7 R_E to oscillate at their eigenperiods. In the region of increasing density near GEOS-2, a relatively highly-damped surface wave is excited. This feeds energy rapidly into a narrow monochromatic toroidal field-line resonance, which subsequently decays more slowly through ionospheric dissipation.     

3D MHD Coronal Oscillations about a Magnetic Null Point: Application of WKB Theory

This paper is a demonstration of how the WKB approximation can be used to help solve the linearised 3D MHD equations. Using Charpit’s method and a Runge?–?Kutta numerical scheme, we have demonstrated this technique for a potential 3D magnetic null point, B=[x,ε y,?(ε+1)z]. Under our cold-plasma assumption, we have considered two types of wave propagation: fast magnetoacoustic and Alfvén waves. We find that the fast magnetoacoustic wave experiences refraction towards the magnetic null point and that the effect of this refraction depends upon the Alfvén speed profile. The wave and thus the wave energy accumulate at the null point. We have found that current buildup is exponential and the exponent is dependent upon ε. Thus, for the fast wave there is preferential heating at the null point. For the Alfvén wave, we find that the wave propagates along the field lines. For an Alfvén wave generated along the fan plane, the wave accumulates along the spine. For an Alfvén wave generated across the spine, the value of ε determines where the wave accumulation will occur: fan plane (ε=1), along the x-axis (0<ε<1) or along the y-axis (ε>1). We have shown analytically that currents build up exponentially, leading to preferential heating in these areas. The work described here highlights the importance of understanding the magnetic topology of the coronal magnetic field for the location of wave heating.     

Dissipation of magnetic flux and magnetic energy in partially ionized gases

Macroscopic equations of motion are used to derive several forms of the generalized Ohm's law for partially ionized ternary gases in magnetic fields, and a conductivity σ is defined that is independent of the magnetic field. A flux theorem is derived using a velocityu _H that can be defined to be the velocity of magnetic field lines;u _H is only slightly different from the velocity of the electron component of the gas. It is shown that σ is the conductivity relevant to the decay of magnetic flux through any surface moving everywhere with velocityu _H . The rate of increase of the thermal energy density of the gas arising through collisions between particles of different species can be resolved into Joule heating at the ratej ²/σ, wherej is the current density, and heating associated with ambipolar drift. The latter, contrary to what has been claimed by some authors, is not necessarily fully compensated by a decrease in the energy of the electromagnetic field. In many applications such compensation does occur, but it may not in interstellar clouds where large amounts of gravitational energy can be made available by collapse, and then both heating and an increase in electromagnetic field energy may occur.     

Canonical and phantom scalar fields as an interaction of two perfect fluids

In this article we investigate and develop specific aspects of Friedmann-Robertson-Walker (FRW) scalar field cosmologies related to the interpretation that canonical and phantom scalar field sources may be interpreted as cosmological configurations with a mixture of two interacting barotropic perfect fluids: a matter component ρ ₁(t) with a stiff equation of state (p ₁=ρ ₁), and an “effective vacuum energy” ρ ₂(t) with a cosmological constant equation of state (p ₂=?ρ ₂). An important characteristic of this alternative equivalent formulation in the framework of interacting cosmologies is that it gives, by choosing a suitable form of the interacting term Q, an approach for obtaining exact and numerical solutions. The choice of Q merely determines a specific scalar field with its potential, thus allowing to generate closed, open and flat FRW scalar field cosmologies.     

Generalized teleparallel gravity via some scalar field dark energy models

We consider generalized teleparallel gravity in the flat FRW universe with a viable power-law f(T) model. We construct its equation of state and deceleration parameters which give accelerated expansion of the universe in quintessence era for the obtained scale factor. Further, we develop correspondence of f(T) model with scalar field models such as, quintessence, tachyon, K-essence and dilaton. The dynamics of scalar field as well as scalar potential of these models indicate the expansion of the universe with acceleration in the f(T) gravity scenario.     

Vaidya black hole in non-stationary de Sitter space: Hawking’s temperature

In this paper we present a class of non-stationary solutions of Einstein’s field equations describing embedded Vaidya-de Sitter black holes with a cosmological variable function Λ(u). The Vaidya-de Sitter black hole is interpreted as the radiating Vaidya black hole is embedded into the non-stationary de Sitter space with variable Λ(u). The energy-momentum tensor of the Vaidya-de Sitter black hole is expressed as the sum of the energy-momentum tensors of the Vaidya null fluid and that of the non-stationary de Sitter field, and satisfies the energy conservation law. We study the energy conditions (like weak, strong and dominant conditions) for the energy-momentum tensor. We find the violation of the strong energy condition due to the negative pressure and leading to a repulsive gravitational force of the matter field associated with Λ(u) in the space-time. We also find that the time-like vector field for an observer in the Vaidya-de Sitter space is expanding, accelerating, shearing and non-rotating. It is also found that the space-time geometry of non-stationary Vaidya-de Sitter solution with variable Λ(u) is Petrov type D in the classification of space-times. We also find the Vaidya-de Sitter black hole radiating with a thermal temperature proportional to the surface gravity and entropy also proportional to the area of the cosmological black hole horizon.     

Interplanetary energy flux associated with magnetospheric substorms

It is shown that the interplanetary quantity ε(t), obtained by Perreault and Akasofu (1978), for intense geomagnetic storms, also correlates well with individual magnetospheric substonns. This quantity is given by $\text{ε(t) = VB}{}^2\text{sin}{}^4\text{(}\text{θ}\text{2}\text{)l}{}_{\mathrm{o}}{}^2$, where V and B denote the solar wind speed and the magnitude of the interplanetary magnetic field (IMF), respectively, and θ denotes the polar angle of the IMF; l_o is a constant ? 7 Earth radii. The AE index is used in this correlation study. The correlation is good enough to predict both the occurrence and intensity of magnetospheric substonns observed in the auroral zone, by monitoring the quantity ε(t) upstream of the solar wind.