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.     

Transit Time of Coronal Mass Ejections under Different Ambient Solar Wind Conditions

The speed [v(R)] of coronal mass ejections (CMEs) at various distances from the Sun is modeled (as proposed by Vr?nak and Gopalswamy in J. Geophys. Res. 107, 2002, doi: 10.1029/2001/JA000120 ) by using the equation of motion a _drag=γ(v?w) and its quadratic form a _drag=γ(v?w)|v?w|, where v and w are the speeds of the CME and solar wind, respectively. We assume that the parameter γ can be expressed as γ=αR ^β , where R is the heliocentric distance, and α and β are constants. We extend the analysis of Vr?nak and Gopalswamy to obtain a more detailed insight into the dependence of the CME Sun–Earth transit time on the CME speed and the ambient solar-wind speed, for different combinations of α and β. In such a parameter-space analysis, the results obtained confirm that the CME transit time depends strongly on the state of the ambient solar wind. Specifically, we found that: i) for a particular set of values of α and β, a difference in the solar-wind speed causes larger transit-time differences at low CME speeds [v ₀], than at high v ₀; ii) the difference between transit times of slow and fast CMEs is larger at low solar-wind speed [w ₀] than at high w ₀; iii) transit times of fast CMEs are only slightly influenced by the solar-wind speed. The last item is especially important for space-weather forecasting, since it reduces the number of key parameters that determine the arrival time of fast CMEs, which tend to be more geo-effective than the slow ones. Finally, we compared the drag-based model results with the observational data for two CME samples, consisting of non-interacting and interacting CMEs (Manoharan et al. in J. Geophys. Res. 109, 2004). The comparison reveals that the model results are in better agreement with the observations for non-interacting events than for the interacting events. It was also found that for slow CMEs (v ₀<500 km?s^?1), there is a deviation between the observations and the model if slow-wind speeds (≈?300?–?400 km?s^?1) are taken for the model input. On the other hand, the model values and the observed data agree for both the slow and the fast CMEs if higher solar-wind speeds are assumed. It is also found that the quadratic form of the drag equation reproduces the observed transit times of fast CMEs better than the linear drag model.     

The big trip and Wheeler-DeWitt equation

Of all the possible ways to describe the behavior of the universe that has undergone a big trip the Wheeler-DeWitt equation should be the most accurate—provided, of course, that we employ the correct formulation. In this article we start by discussing the standard formulation introduced by González-Díaz and Jimenez-Madrid, and show that it allows for a simple yet efficient method of the solution’s generation, which is based on the Moutard transformation. Next, by shedding the unnecessary restrictions, imposed on aforementioned standard formulation we introduce a more general form of the Wheeler-DeWitt equation. One immediate prediction of this new formula is that for the universe the probability to emerge right after the big trip in a state with w=w ₀ will be maximal if and only if w ₀=−1/3.     

Om diagnostic for viscous Cardassian universe

Om diagnostic is a useful geometric method to differentiate between different cosmological models without the accurate current value of matter density. We investigate the Om diagnostic for viscous Cardassian universe and find that the model can be easily distinguished from LCDM. We also investigate the influence of the bulk viscosity coefficient τ on the evolutive behavior of Om with respect to redshift z. According to the value of Om(z=0) for viscous Cardassian models, we obtain the current value of equation of state w _k0.     

On a family of well behaved perfect fluid balls as astrophysical objects in general relativity

A family of well behaved perfect fluid balls has been derived starting with the metric potential g ₄₄=B(1+Cr ²) ⁿ for all positive integral values of n. For n≥4, the members of this family are seen to satisfy the various physical conditions e.g. c ² ρ≥p≥0,dp/dr<0,dρ/dr<0, along with the velocity of sound \((\sqrt{dp/c^{2}d\rho} )< 1\) and the adiabatic index ((p+c ² ρ)/p)(dp/(c ² dρ))>1. Also the pressure, energy density, velocity of sound and ratio of pressure and energy density are of monotonically decreasing towards the pressure free interface (r=a). The fluid balls join smoothly with the Schwarzschild exterior model at r=a. The well behaved perfect fluid balls so obtained are utilised to construct the superdense star models with their surface density 2×10¹⁴  gm/cm³. We have found that the maximum mass of the fluid balls corresponding to various values of n are decreasing with the increasing values of n. Over all maximum mass for the whole family turns out to be 4.1848M _Θ and the corresponding radius as 19.4144 km while the red shift at the centre and red shift at surface as Z ₀=1.6459 and Z _a =0.6538 respectively this all happens for n=4. It is interesting to note that for higher values of n viz n≥170, the physical data start merging with that of Kuchowicz superdense star models and hence the family of fluid models tends to the Kuchowicz fluid models as n→∞. Consequently the maximum mass of the family of solution can not be less than 1.6096 M _Θ which is the maximum mass occupied by the Kuchowicz superdense ball. Hence each member of the family for n≥4 provides the astrophysical objects like White dwarfs, Quark star, typical neutron star.     

Cosmological evolution of agegraphic dark energy with the sign-changeable interaction

In this paper, we study a cosmological model with the sign-changeable interaction between agegraphic dark energy (ADE) and dark matter. For the accelerated expansion of the universe, the model parameters n and β should satisfy the condition n>1 and $-\frac{2}{3}<\beta<0$ . We also investigate the effect of the parameters n and β on the evolutive behavior of our universe. Furthermore, by analysis it is shown that the equation of state of ADE with the sign-changeable interaction can cross the phantom divide from w _d >?1 to w _d <?1 for the appropriate n and β. This is different from that of ADE with usual interaction, whose equation of state changes from w _d <?1 to w _d >?1.     

Bianchi type-V cosmological models with perfect fluid and dark energy

We consider a self-consistent system of Bianchi type-V cosmology and binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be one obeying the usual equation of state p=γ ρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or Chaplygin gas. Exact solutions to the corresponding Einstein equations are obtained as a quadrature. The cases of disordered radiation and models with power-law and exponential expansion have discussed in detail. For large t, the models tend to be isotropic.     

The sign-changeable interaction between variable generalized Chaplygin gas and dark matter

In this paper, we study a cosmological model with the sign-changeable interaction between variable generalized Chaplygin gas (VGCG) and dark matter. The dynamical analysis indicates that there exists a stable scaling attractor, which can help to alleviate the coincidence problem. Furthermore, when the parameters of the model take some fixed values, the attractor corresponds to the phase w=?0.939 and the equation of state of VGCG approaches it from either w>?1 or w<?1 depending on the choice of its initial cosmic density parameter and the ratio of pressure to critical energy density. So, the phantom divide can be crossed. We find the interaction term Q can change its sign from Q<0 to Q>0 as the universe expands, which is different from the usual interaction. Also, we place constraints on the parameters from the point of view of dynamics.     

Testing Cosmological Models using the Kinematics of High Redshift Galaxies

The scaling of the apparent angular diameter of galaxies with redshift θ(z) is a powerful discriminator of cosmological models. In this paper we argue that the rotational velocity of distant galaxies, when interpreted as size indicator, may be used as an interesting tool to select high redshift standard rods. Upcoming deep redshift surveys will allow an implementation of this classical geometrical test to measure directly the amplitude of the cosmological constant Λ, or to constrain the cosmic equation of state parameter for a smooth dark energy component (w = p/ρ, —1 ≤ w < 0).     

The solution of radiation transfer problem for a slab with space-dependent albedo and anisotropic scattering

The transport of thermal radiation has been considered within a finite slab which absorb and scatter anisotropically. The problem involves the space-dependent single-scattering albedow(x). Two approximations are taken forw(x). In the first it is represented in exponential form asw(x)=w ₀ exp(–x/s), wherew ₀ ands are given constants andx is the optical variable. The second approximation assumes the formw(x) = _r=0 ^R d _r ^* p _r (x/a), whered _r ^* are known expansion coefficients anda is the half optical thickness of the slab. Analytic expressions for the forward, backward radiation intensities and fluxes are given in each approximation. The solution of the linear transport equation is performed on the basis of integral Fourier transforms.     

Generalized Chaplygin gas model with or without viscosity in the w–w′ plane

In this paper, we investigate the dynamics of generalized Chaplygin gas (GCG) model with or without viscosity in the w–w′ plane, which is defined by the equation of state parameter and its time derivative with respect to the logarithm of the scale factor. We show that GCG model without viscosity approaches to a late time de Sitter attractor (w _g =−1) and behaves like a “freezing” scalar field for the parameter α constrained by the latest observational data. However, introducing viscosity exerts an influence on the evolution of w and affects the location of the late time attractor (w _g >−1) in viscous GCG model. We also find numerically such a transition from w′>0 to w′<0 as the universe expands in viscous GCG model different from GCG model without viscosity (w′<0) in the w–w′ plane.     

A new type of interaction between generalized Chaplygin gas and dark matter

In this paper, we investigate the model with a new type of interaction between generalized Chaplygin gas (GCG) and dark matter. It is shown that there exists a stable scaling attractor, which provides the possibility to alleviate the coincidence problem. The equation of state (EoS) of GCG approaches the attractor phase from either w _g >?1 or w _g w _g w _g w _g >?1), and next cross again the phantom divide (the transition from w _g >?1 to w _g Q can change its sign from Q<0 to Q>0 as the universe expands, which is different from the usual interaction. Moreover, we investigate the model from statefinder viewpoint. The statefinder diagnostic can not only discriminate the model with different coupling constant but also distinguish the model from other dark energy models.     

A class of well-behaved generalized charged analogues of Vaidya-Tikekar type fluid sphere in general relativity

In this paper first ever we have developed a class of well behaved charged fluid spheres expressed by a space time with its hypersurfaces $t = \operatorname {const}$ . as spheroid for the case 0<K<1 with surface density 2×10¹⁴ gm/cm³. The same utilized to construct a superdense star and seen that star satisfies all well behaved condition for 0<K≤0.038. The maximum mass occupied and the corresponding radius are found to be 4.830982M _Θ and 20.7612 km respectively. The redshift at the center and on the surface is given z ₀=0.425367 and z _a =0.240901.     

New agegraphic dark energy model with the sign-changeable interaction

In this paper, we investigate a cosmological model with the sign-changeable interaction between new agegraphic dark energy (NADE) and dark matter. By analysis it is shown that the equation of state (EoS) of NADE can cross the phantom divide under the condition of the model parameter β<0. In addition, we plot the trajectories of the interacting NADE model for different values of the parameters n and β in the statefinder plane. It is found that the statefinder trajectories can be distinguished by both n and β. Furthermore, we study the interacting NADE model by means of the w?w′ analysis.     

Observational study of higher dimensional magnetic universe in non-linear electrodynamics

In this work, we have considered the flat FRW model of the universe in (n+2)-dimensions filled with the dark matter and the magnetic field. We present the Hubble parameter in terms of the observable parameters Ω _m0 and H ₀ with the redshift z and the other parameters like B ₀, ω, μ ₀, δ, n, w _m . The natures of magnetic field B, deceleration parameter q and $\operatorname{Om}$ diagnostic have also been analyzed for accelerating expansion of the universe. From Stern data set (12 points), we have obtained the bounds of the arbitrary parameters by minimizing the χ ² test. The best-fit values of the parameters are obtained by 66 %, 90 % and 99 % confidence levels. Now to find the bounds of the parameters (B ₀,ω) and to draw the statistical confidence contour, we fixed four parameters μ ₀, δ, n, w _m . Here the parameter n determines the higher dimensions and we perform comparative study between three cases: 4D (n=2), 5D (n=3) and 6D (n=4) respectively. Next due to joint analysis with BAO observation, we have also obtained the bounds of the parameters (B ₀,ω) by fixing other parameters μ ₀, δ, n, w _m for 4D, 5D and 6D. The best fit of distance modulus for our theoretical model and the Supernova Type Ia Union2 sample are drawn for different dimensions.     

Overtaking collision of two ion acoustic soliton in a plasma with a q-nonextensive electron and thermal positrons

Theoretically the propagation of two ion acoustic soliton interaction in a three component collisionless unmagnetized plasma which consists of electrons, positrons and cold ions, has been investigated here by employing reductive perturbation technique. In this study, q distributed electrons and Maxwell-Boltzmann distributed positrons are considered and Korteweged-de Vries (KdV) equation is derived. The KdV equation is solved to get two soliton solution by using Hirota bilinear method. The effects of the q distributed electrons on the profiles of two soliton structures and the corresponding phase shifts are investigated. It is observed that both the nonextensive parameter (q) and the ratio of positrons density and electron density (p=n _p0/n _e0), play a significant role in the formation and existence of two soliton and also in the nature of their phase shifts.     

Robust resolution of Kepler’s equation in all eccentricity regimes

The singularity for the big bang state can be represented using the generalized anisotropic Friedmann equation, resulting in a system of differential equations in a central force field. We study the regularizability of this singularity as a function of a parameter, the equation of state, w. We prove that for w > 1 it is regularizable only for w satisfying relative prime number conditions, and for w ≤ 1 it can always be regularized. This is done by using a McGehee transformation, usually applied in the three and four-body problems. This transformation blows up the singularity into an invariant manifold. The relationship of this result to other cosmological models is briefly discussed.     

The prospects for life on Mars: A pre-Viking assessment

Mariner 9 has provided a refutation or reinterpretation of several historical claims for Martian biology, and has permitted an important further characterization of the environmental constraints on possible Martian organisms. Four classes of conceivable Martian organisms are identified, depending on the environmental temperature, T, and water activity, a_w: Class I, high T, high a_w; Class II, low T, high a_w; Class III, high T, low a_w; and Class IV, low T, low a_w. The Viking lander biology experiments are essentially oriented toward Class I organisms, although arguments are given for the conceivable presence on Mars of organisms in any of the four classes. Organisms which extract their water requirements from hydrated minerals or from ice are considered possible on Mars, and the high ultraviolet flux and low oxygen partial pressure are considered to be negligible impediments to Martian biology. Large organisms, possibly detectable by the Viking lander cameras, are not only possible on Mars; they may be favored. The surface distribution of Martian organisms and future search strategies for life on Mars are discussed.