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.     

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.     

The K * Kπ and ρππ couplings in QCD

The light cone QCD sum rules are derived for the K ^* Kπ coupling g _K ^* Kπ and the ρππ coupling g _ρππ. The contribution from the excited states and the continuum is subtracted cleanly through the double Borel transform with respect to the two external momenta, p ₁ ², p ₂ ²= (p−q)². Our result g _K ^* Kπ= (8.7 ± 0.5) and g _ρππ= (11.5 ± 0.8) is in good agreement with the experimental value. Received: 31 July 1998 / Revised version: 20 November 1998     

<Emphasis Type="Italic">C</Emphasis>-field Cosmological Models with Variable <Emphasis Type="Italic">G</Emphasis> in FRW Space–Time

C-field cosmological models based on Hoyle-Narlikar theory with variable gravitational constant G in the frame work of FRW (Friedmann-Robertson-Walker) space–time for positive and negative curvatures are investigated. To get the deterministic solutions in terms of cosmic time t, we have assumed G=R ⁿ and discussed for n=−1, −2, R being scalar factor. In both the cases, creation field C increases with time, the gravitational constant G and matter density (ρ) decrease with time in the model (21). In the model (41) G decreases with time and matter density (ρ) is constant. The other physical aspects of the models are also 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.     

Spherically symmetric static solutions of the Einstein-Maxwell equations

We report a new formalism to obtain solutions of Einstein-Maxwell’s equations for static spheres assuming the matter content to be a charged perfect fluid of null-conductivity. Defining three new variablesu=4πεr ²,ν=4πpr ^{2 2} andw=(4π/3)(ρ+ε)r ² whereε, ρ andε denote respectively energy densities of the electric, matter and free gravitational fields whereasp is the fluid pressure, Einstein’s field equations are rewritten in an elegant form. The solutions given by Bonnor [1], Nduka [2], Cooperstock and De la Cruz [3], Mehra [4], Tikekar [5,6], Xingxiang [7], Patino and Rago [8] are all shown to possess simple relations betweenu, v, andw whereas Pant and Sah’s [9] solution for which all the three functions,u, v, andw are constants is a trivial case of the present formalism, We have presented six new solutions with ε = 2ρ. For the first three solutionsw andu are constants withv as a variable whereas the remaining three solutions satisfy the equation of state for isothermal gas;v =kw =-ku where (i)k is an arbitrary constant but not equal to 1 or 1/3 (ii)k = 1 and (iii)k = 1/3. We also obtained a generalization of Cooperstock and De la Cruz’s [3] solution which is regular for 2ρ > ε but singular for 2ρ ≤ ε.     

SCQGP in quark stars

From an analogy with non-relativistic degenerate QED plasma we make an estimate of the coupling strength of QGP hypothesized to be present in compact star interiors. At densities ranging from 3ρ ₀–10ρ ₀ (normal nuclear density ρ ₀=0.16 fm⁻³), quark matter is found to be strongly to intermediately coupled. The equation of state for QED plasma obtained via Pade approximation, modified to QGP, yields stable stellar sequences with maximum mass ≳2M _⊙ for B ^1/4≲215 MeV.     

Naked singularity formation in $${f({\mathcal R})}$$ gravity

We study the gravitational collapse of a star with barotropic equation of state p = wρ in the context of f(R){f({\mathcal R})} theories of gravity. Utilizing the metric formalism, we rewrite the field equations as those of Brans-Dicke theory with vanishing coupling parameter. By choosing the functionality of Ricci scalar as f(R)=aR^m{f({\mathcal R})=\alpha{\mathcal R}^{m}} , we show that for an appropriate initial value of the energy density, if α and m satisfy certain conditions, the resulting singularity would be naked, violating the cosmic censorship conjecture. These conditions are the ratio of the mass function to the area radius of the collapsing ball, negativity of the effective pressure, and the time behavior of the Kretschmann scalar. Also, as long as parameter α obeys certain conditions, the satisfaction of the weak energy condition is guaranteed by the collapsing configuration.     

How to measure the pomeron phasein diffractive dipion photoproduction

The study of charge asymmetry of pions in the high-energy process ep → eπ⁺π^-p (γp → π⁺π^-p) at very small dipion momenta offers a method to measure the phase of the forward hadronic (quasi-) elastic amplitude γp → ρp. We estimate the potential of such measurements at HERA. Received: 19 February 2004, Revised: 1 August 2005, Published online: 3 November 2005     

Anisotropic Universe Models with Perfect Fluid and Dark Energy with Time Varying G and Λ

We have investigated general Bianchi type I cosmological models which containing a perfect fluid and dark energy with time varying G and Λ that have been presented. The perfect fluid is taken to be one obeying the equation of state parameter, i.e., p=ωρ; whereas the dark energy density is considered to be either modified polytropic or the Chaplygin gas. Cosmological models admitting both power-law which is explored in the presence of perfect fluid and dark energy too. We reconstruct gravitational parameter G, cosmological term Λ, critical density ρ _c , density parameter Ω, cosmological constant density parameter Ω _Λ and deceleration parameter q for different equation of state. The present study will examine non-linear EOS with a general nonlinear term in the energy density.     

Realizability of Point Processes

There are various situations in which it is natural to ask whether a given collection of k functions, ρ _j (r ₁,…,r _j ), j=1,…,k, defined on a set X, are the first k correlation functions of a point process on X. Here we describe some necessary and sufficient conditions on the ρ _j ’s for this to be true. Our primary examples are X=ℝ ^d , X=ℤ ^d , and X an arbitrary finite set. In particular, we extend a result by Ambartzumian and Sukiasian showing realizability at sufficiently small densities ρ ₁(r). Typically if any realizing process exists there will be many (even an uncountable number); in this case we prove, when X is a finite set, the existence of a realizing Gibbs measure with k body potentials which maximizes the entropy among all realizing measures. We also investigate in detail a simple example in which a uniform density ρ and translation invariant ρ ₂ are specified on ℤ; there is a gap between our best upper bound on possible values of ρ and the largest ρ for which realizability can be established.     

Inflationary Phase in a Generalized Brans-Dicke Theory

We find a solution for exponential inflation in a Brans-Dicke generalized model, where the coupling “constant” is variable. While in General Relativity the equation of state is p=−ρ, here we find p=α ρ, where α<−2/3. The negativity of cosmic pressure implies acceleration of the expansion, even with Λ<0.     

Bianchi Type-III Cosmological Models with Time Dependent Displacement Vector for Barotropic Fluid Distribution in Lyra Geometry

Bianchi Type-III cosmological models for perfect fluid distribution with time dependent displacement field in the framework of Lyra geometry are investigated. To get the deterministic model of the universe, we have assumed two conditions (i) shear (σ) is proportional to the expansion (θ). This leads to B=C ⁿ where B and C are metric potentials and n is a constant. (ii) Universe is filled with barotropic fluid distribution which leads to p=γ ρ, 0≤γ≤1, p being isotropic pressure and ρ the energy density. The physical and geometrical aspects of the model with a special case and singularities in the models are also discussed.     

Shock profiles for the asymmetric simple exclusion process in one dimension

The asymmetric simple exclusion process (ASEP) on a one-dimensional lattice is a system of particles which jump at ratesp and 1-p (herep > 1/2) to adjacent empty sites on their right and left respectively. The system is described on suitable macroscopic spatial and temporal scales by the inviscid Burgers’ equation; the latter has shock solutions with a discontinuous jump from left density ρ- to right density ρ+, ρ-< ρ +, which travel with velocity (2p−1 )(1−ρ₊−p ₋). In the microscopic system we may track the shock position by introducing a second class particle, which is attracted to and travels with the shock. In this paper we obtain the time-invariant measure for this shock solution in the ASEP, as seen from such a particle. The mean density at lattice siten, measured from this particle, approachesp _± at an exponential rate asn→ ±∞, witha characteristic length which becomes independent ofp when . For a special value of the asymmetry, given byp/(1−p)=p ₊(1−p ₋)/p ₋(1−p ₊), the measure is Bernoulli, with densityρ ₋ on the left andp ₊ on the right. In the weakly asymmetric limit, 2p−1 → 0, the microscopic width of the shock diverges as (2p+1)^-1. The stationary measure is then essentially a superposition of Bernoulli measures, corresponding to a convolution of a density profile described by the viscous Burgers equation with a well-defined distribution for the location of the second class particle.     

Dissipative Future Universe Without Big Rip

The present study deals with dissipative future universe without big rip in context of Eckart formalism. The generalised Chaplygin gas, characterised by equation of state p=-\fracAr^\frac1ap=-\frac{A}{\rho^{\frac{1}{\alpha}}}, has been considered as a model for dark energy due to its dark-energy-like evolution at late time. It is demonstrated that, if the cosmic dark energy behaves like a fluid with equation of state p=ωρ; ω<−1 as well as Chaplygin gas simultaneously then the big rip problem does not arise and the scale factor is found to be regular for all time.     

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→±∞.     

Gravity waves accompanying supernova explosions

Gravitational radiation arising during the formation of a protoneutron star is studied. Here it is mainly large-scale nonuniformities that develop inside the star. The entropy and density profiles of such nonuniformities resemble the “mushroom cloud” of a nuclear explosion. A bubble of hot neutron matter floats to the surface of the star, like the “mushroom cloud” of an explosion in the earth’s atmosphere. Depending on the symmetry of the problem, from two to six bubbles can float upward at the same time. The characteristic masses of such bubbles are 0.01M _⊗ and the radial velocities reach ∼0.1c. The energy radiated in the form of gravitational waves in one cycle of bubbles floating to the surface is ∼10⁻² M _⊗ c ²−10⁻¹⁰ M _⊗ c ². Such cycles occur repeatedly as the neutron star cools. This phase can last up to seconds. The total energy radiated in the form of gravitational radiation can reach 10⁻¹ M _⊗ c ². Pis’ma Zh. éksp. Teor. Fiz. 64, No. 12, 817–822 (25 December 1996)     

On the thermodynamic properties of the quantum vacuum

Several thermodynamic relations for the vacuum state have been derived by assuming that it behaves like a relativistic perfect simple fluid. Unlike the usual fluids, the vacuum becomes hotter when it undergoes an adiabatic expansion (TV ⁻¹=const). A new Lorentz-invariant spectrum for the vacuum is also suggested which is compatible with the usual equation of statep=−ρ and the other thermodynamic constraints. Some cosmological consequences of these results have also been discussed.