Bianchi Type V Barotropic Perfect Fluid Cosmological Model in Lyra Geometry

We have investigated Bianchi Type V barotropic perfect fluid cosmological model in Lyra geometry. To get the deterministic model of the universe, we have assumed the barotropic perfect fluid condition p=γ ρ, 0≤γ≤1 and energy conservation equation i.e. T _i;j ^j =0. The physical and geometrical aspects of the model are discussed. The special cases for γ=1 (stiff fluid distribution), γ=0 (dust distribution), γ=1/3 (disordered radiation) are also discussed.     

Bianchi Type III Cosmological Models for Barotropic Perfect Fluid Distribution with Variable <Emphasis Type="Italic">G</Emphasis> and <Emphasis Type="BoldItalic">Λ</Emphasis>

Bianchi type III cosmological model for perfect fluid distribution with variable G and Λ are investigated. To get the determinate models, we have assumed the barotropic condition p=γ ρ and shear (σ) is proportional to expansion (θ) where p is isotropic pressure, ρ the matter density and 0≤γ≤1. The physical and geometrical aspects related with the observations and singularities in the models are discussed.     

Bianchi Type-III Bulk Viscous and Barotropic Perfect Fluid Cosmological Models in Lyra’s Geometry

We have investigated Bianchi type III bulk viscous and barotropic perfect fluid cosmological models in the frame work of Lyra’s geometry. To get deterministic models of universe, we have assumed the three conditions: (i) shear scalar (σ) is proportional to the expansion (θ). This leads to B=C ⁿ , where B and C are metric potentials. (ii) In presence of viscous fluid, the coefficient of viscosity of dissipative fluid is a power function of mass density ξ=ξ ₀ ρ ^m , where ξ ₀ and m are constant and (iii) in absence of viscosity, a proportionality relation between pressure and energy density of barotropic perfect fluid p=αρ, where α is a proportionality constant. In all the cases, we observed that the displacement vector β is large at beginning of the universe and reduces fast during its evolution so that its nature coincide with the behavior of cosmological constant Λ.     

Gravitational collapse in higher dimensional Husain space–time

We investigate exact solution in higher dimensional Husain model for a null fluid source with pressure p and density ρ are related by the following relations (i) p  =  kρ, (ii) (variable modified Chaplygin) and (iii) p  =  kρ^α (polytropic). We have studied the nature of singularity in gravitational collapse for the above equations of state and also for different choices of the of the parameters k and B namely, (i) k  =  0, B  =  constant (generalized Chaplygin), (ii) B  =  constant (modified Chaplygin). It is found that the nature of singularity is independent of these choices of different equation of state except for variable Chaplygin model. Choices of various parameters are shown in tabular form. Finally, matching of Szekeres model with exterior Husain space–time is done.     

Gravitational Collapse without a Remnant

We investigate the gravitational collapse of a spherically symmetric, inhomogeneous star, which is described by a perfect fluid with heat flow and satisfies the equation of state p=ρ/3 or p=C ρ ^γ at its center. Different from the ordinary process of gravitational collapsing, the energy of the whole star is emitted into space. And the remaining spacetime is a Minkowski one at the end of the process.     

Magnetized Domain Walls Cosmological Model in General Relativity

A non-static Bianchi type-III domain walls cosmological models in presence and absence of magnetic field are investigated in general theory of relativity. We assume that F ₁₂ is only the non-vanishing component of F _ij . To obtain deterministic model, we assume relations B=C ⁿ and ρ=p. Some physical properties of these models are discussed.     

Charged sphere of shear-free fluids with $$\frac{\partial}{\rho} \partial r \leq 0$$

The Einstein-Maxwell equations for non-static charged shear-free spherically symmetric perfect fluid distribution reduce to a second-order non-linear differential equation in the radial parameter. Several solutions of this equation have been obtained in earlier work without considering the general requirement for physical relevance of the solutions. Generally physically acceptable relativistic fluid models demand that the solutions satisfy the reality conditions ρ ≥ 0, p ≥ 0, ρ _r ≤ 0, etc. throughout the fluid model. In this article the expression for density gradient ρ _x (or ρ _r ) has been utilized to produce charged shear-free relativistic fluid models with non-positive density gradient (NDG)ρ _r ≤ 0. Eventually, we have found that none of the Riccati solutions have NDG including Vaidya metric. Also, the solutions with NDG neither possess Lie-symmetries nor Painlevé property. Further, it is observed that the solutions with NDG have no uncharged analogue.     

Higher Dimensional Bianchi Type-V Cosmological Models with Perfect Fluid and Dark Energy

We have studied the Bianchi type-V cosmological models with binary mixture of perfect fluid and dark energy in five dimensions. The perfect fluid is obeying the equation of state p=γρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or the Chaplygin gas. The exact solutions of the Einstein’s field equations are obtained in quadrature form.     

A Priori Estimates for the Free-Boundary 3D Compressible Euler Equations in Physical Vacuum

We prove a priori estimates for the three-dimensional compressible Euler equations with moving physical vacuum boundary, with an equation of state given by p(ρ) = C _γ ρ ^γ for γ > 1. The vacuum condition necessitates the vanishing of the pressure, and hence density, on the dynamic boundary, which creates a degenerate and characteristic hyperbolic free-boundary system to which standard methods of symmetrizable hyperbolic equations cannot be applied.     

Dark Energy with Generalized Equation of State in Bianchi Type-I Cosmological Model

Dark energy with the usually used equation of state p=γρ, where γ=const<0 is hydrodynamically unstable. To overcome this drawback we consider the cosmology of a perfect fluid with a linear equation of state of a more general form p=α(ρ−ρ ₀), where the constants α and ρ ₀ are free parameters. The anisotropic Bianchi type-I cosmological model filled with dark energy has been considered. A generalized equation of state for the dark energy component of the universe has been used. The exact solutions to the corresponding Einstein field equations and the statefinder diagnostic pair i.e. {r,s} parameters have been obtained in three interesting cases (i) when ρ _Λ>0 and A>0 (ii) when ρ _Λ>0 and A<0 and (iii) when ρ _Λ<0 and A>0 at the singularities i.e. t→0 and t→±∞.     

η(1475) and <Emphasis Type="Italic">f</Emphasis><Subscript>1</Subscript>(1420) resonances in the decay processes <Emphasis Type="Italic">J</Emphasis>/ψ → γ(ρρ, γρ<Superscript>0</Superscript>, γϕ) and in γγ* collisions

A scenario that removes the contradiction between the suppression of the η(1475) → γγ decay width and the strong coupling of η(1475) to the ρρ, ωω, and γρ⁰ channels and which leads to a nontrivial prediction for the manifestation of η(1475) in γγ*(Q ²) collisions is considered. Data on the dependence of the cross section for the reaction γγ*(Q ²) → K[`(K)]pK\bar K\pi on the photon virtuality in the energy range 1.35–1.55 GeV are explained here by the production of an η(1475) resonance in contrast to their standard interpretation in terms of the f <sub>1</sub>(1420) resonance. Experimental verification of the present explanation requires determining the spin-parity of resonance contributions, R, in the reactions γγ*(Q <sup>2</sup>) R → R → K[`(K)]pK\bar K\pi and J/ψ → γR → γ(γρ⁰, γϕ).     

Isospin symmetry breaking in ρ→πγ decay

In terms of effective field theory and mixed-propagator approach, we show that there is a larger hidden effect of isospin breaking in ρ→πγ decay due to a ω exchange, ρ→ω→πγ. The branching ratio is predicted as B(ρ→πγ) = (11.67±2.0)×10^-4, which is much larger than Particle Data Group's datum (6.8±1.7)×10^-4 and one of charged mode, B(ρ^±→π^±γ) = (4.5±0.5)×10^-4. Received: 7 January 2002 / Accepted: 2 April 2002     

Bianchi Type-III Cosmic Strings and Domain Walls Cosmological Model in General Relativity

Bianchi type-III space time is considered in the presence of cosmic strings and thick domain walls source in the frame work of general relativity. Exact cosmological models using various cases of ρ=α λ and p=γ ρ are presented. It is observed that the behavior of these models (with cosmic strings and domain walls), based on their physical and kinematical properties, is found to be identical.     

Cosmological Models with Variable <Emphasis Type="Italic">G</Emphasis> in <Emphasis Type="Italic">C</Emphasis>-Field Cosmology

Cosmological models with variable G in C-field cosmology for barotropic fluid distribution in FRW space-time are investigated. To get the deterministic model of the universe, we have assumed that G=R ⁿ where R is the scale factor and n the constant. To obtain the results in terms of cosmic time t, we have assumed n=−1. We find that for n=−1, Creation field (C) and spatial volume increase with time, G and ρ (matter density) decreases with time, the model represent accelerating universe. Thus inflationary scenario exists in the model. The model is also free from horizon. The results so obtained match with the astronomical observations.     

A Class of Well Behaved Charged Analogues of Schwarzchild’s Interior Solution

A class of well behaved charged analogues of Schwarzchild’s interior solution has been obtained using a particular electric intensity. The solutions of this class are utilized to depict a superdense star model with surface density 2×10¹⁴ g cm⁻³. The solution obtained is new and the pressure (p), density (c ² ρ), velocity of sound and (p/(c ² ρ)) are monotonically decreasing towards the pressure free interface. Moreover the adiabatic constant is found to be more than (4/3) which is necessary for stability under radial perturbation. Also the electric intensity increases monotonically towards the surface. The well behaved model has the maximum mass M=1.740793M _Θ , Radius 12.130308 km. The redshift at the center and on the surface is given by z ₀=0.384261 and z _a =0.292489. Out of the models of superdense star obtained couple of models represent Vela Pulsar for (i) α ²=1.03, b=0.33, , Radius=10.8566 km, M=1.18331M _Θ , I=0.642601×10⁴⁵, (ii) α ²=1.1, b=0.3, , Radius=11.197533 km, M=1.311438M _Θ , I=0.774508×10⁴⁵. All the solutions mentioned above are reducible to Schwarzchild interior solution in the absence of charge.     

Five Dimensional Axially Symmetric String Cosmological Models with Bulk Viscous Fluid

Bulk viscous fluid distribution with massive strings in LRS Bianchi type-1 space time is studied. The exact solutions of the field equations are obtained by using the equation of state ρ=−λ and ρ=λ. We observed that the bulk viscous fluid does not survive for ρ=−λ whereas it survives for ρ=λ. Some physical and geometrical properties of the models are discussed.     

Bianchi type-V model with a perfect fluid and A-term

A self-consistent system of gravitational field with a binary mixture of perfect fluid and dark energy given by a cosmological constant has been considered in Bianchi Type-V universe. The perfect fluid is chosen to be obeying either the equation of state p=γρ with γ ε |0,1| or a van der Waals equation of state. The role of A-term in the evolution of the Bianchi Type-V universe has been studied.     

Cylindrically symmetric matter distribution with a magnetic field in Einstein-Cartan theory

In this paper we have extended our earlier studies of solutions of Einstein-Cartan equations to the case where a magnetic field co-exists with the matter distribution. We have obtained an exact solution of Einstein-Cartan-Maxwell equations representing a static cylinder of perfect fluid with an axial magnetic fieldH and a non-zero spin densityK, satisfying the equation of stateρ=γ(p _r +p _s −H ²/4π),γ being a constant. We notice that as a consequence of field equations there exists a direct relation between the pressurep, and the spin densityK, indicating that an increase in pressure would enormously increase the spin density. Alexander von Humboldt Research Fellow.