Junction conditions and consequences of quasi-spherical space-time with electro-magnetic field and Vaidya metric

In this work the junction conditions between the exterior Reissner-Nordstrom-Vaidya space-time with the interior quasi-spherical Szekeres space-time have been studied for analyzing gravitational collapse in the presence of a magneto-hydrodynamic fluid undergoing dissipation in the form of heat flow. We have discussed about the apparent horizon and have evaluated the time difference between the formation of apparent horizon and central singularity.      

Anisotropic spheres with uniform energy density in bimetric theory of relativity

In this paper we have obtained interior solutions of the field equations for anisotropic sphere in the bimetric general relativity theory formulated by Rosen (Lett. Nuovo Cimento 25, 1979). A class of solutions for a uniform energy-density source of the field equations is presented. The analytic solutions obtained are physically reasonable, well behaved in the interior of the sphere. The solutions agree with the Einstein’s general relativity for a physical system compared to the size of the universe such as the solar system.     

Uniform radial motion of sound in a relativistic fluid ball

We present a new class of spherically symmetric exact solutions of the general relativistic field equations. These solutions describe perfect fluid balls with infinite central pressure and central density though their ratio is finite. A member of the class has been studied in detail from which we have constructed a model of causal fluid ball with constant sound speed.     

A new class of relativistic stellar models

Einstein field equations for a static and spherically symmetric perfect fluid are considered. A formulation given by Patiño and Rago is used to obtain a class of nine solutions, two of them are Tolman solutions I, IV and the remaining seven are new. The solutions are the correct ones corresponding to expressions derived by Patiño and Rago which have been shown by Knutsen to be incorrect. Similar to Tolman solution IV each of the new solutions satisfies energy conditions inside a sphere in some range of two independent parameters. Besides, each solution could be matched to the exterior Schwarzschild solution at a boundary where the pressure vanishes and thus the solutions constitute a class of new physically reasonable stellar models.     

The general class of Bianchi cosmological models with viscous fluid and particle creation in Brans-Dicke theory

This paper deals with the general class of Bianchi cosmological models with bulk viscosity and particle creation described by full causal thermodynamics in Brans-Dicke theory. We discuss three types of average scale-factor solutions for the general class of Bianchi cosmological models by using a special law for the deceler- ation parameter which is linear in time with a negative slope. The exact solutions to the corresponding field equations are obtained in quadrature form and solutions to the Einstein field equations are obtained for three different physically viable cosmologies. All the physical parameters are calculated and discussed in each model.     

Relativistic collapsing radiating stars

A new class of exact solutions of Einstein’s equations is proposed for a collapsing radiating spherically symmetric shear-free isotropic fluid undergoing radial heat flow. In remote past the solutions are static perfect fluid which then gradually starts evolving into radiating collapse. The interior solutions are matched with Vaidya exterior metric over the boundary.     

A class of new Bianchi I perfect fluid space-times

A procedure to generate new exact solutions to Einstein equations for perfect fluids is applied to LRS Bianchi type I line-element. Starting from some known solutions a class of new perfect fluid solutions of Bianchi type I are presented. The physical and kinematical properties of spatially homogeneous and anisotropic cosmological models are studied.     

Nonsingular charged analogues of Schwarzschild’s interior solution

The problem of finding nonsingular charged analogue of Schwarzschild’s interior solutions has been reduced to that of finding a monotonically decreasing function f. The models are discussed in generality by imposing reality condition on f. It is shown that the physical solutions are possible only for surface density to central density ratio greater than or equal to 2/3 i.e. $\frac{\rho_{a}}{\rho_{0}}\ge2/3$ . The unphysical nature of solutions with linear equation state has been proved. A generalization procedure has been utilized to generalize solutions by Guilfoyle (1999). Recently found solutions by Gupta and Kumar (2005a, 2005b, 2005c) are generalized by taking particular form of f and seen to have higher mass and more stable. The maximum mass is found to be 1.59482 M _Θ . The models have been found to be stable once the physical requirements are established due to mass to radius less than 4/9, total charge to total mass ratio less than 1 and redshift quite low.     

New exact cosmologies on the brane

We develop a method for constructing exact cosmological solutions in brane world cosmology. New classes of cosmological solutions on Randall–Sandrum brane are obtained. The superpotential and Hubble parameter are represented in quadratures. These solutions have inflationary phases under general assumptions and also describe an exit from the inflationary phase without a fine tuning of the parameters. Another class solutions can describe the current phase of accelerated expansion with or without possible exit from it.     

A new class of bulk viscous cosmological models in a scale covariant theory of gravitation

Field equations of cosmological models with bulk viscosity are constructed in the scale covariant theory of gravitation. A new class of solutions for the model is found by applying a variable deceleration parameter. Some physical implications of these solutions are briefly discussed.     

Plane symmetric inhomogeneous cosmological models with a perfect fluid in General Relativity II

We investigate a class of solutions of Einstein equations for the plane symmetric perfect fluid case. If these solutions have shear, they must necessarily be non-static. Some physical and geometric properties of the models are also discussed.      

Cosmological electrovac model in Bertotti-Robinson space-time

Cosmological electrovac field equations are studied in Bertotti-Robinson-type space-time, and a class of cosmological solutions is obtained. The nature of the electromagnetic fields and singularities of the solution is studied. A technique is established to generate these solutions from a known vacuum solution with a non-zero cosmological constant.     

Plane Symmetric Cosmological Model with Quark and Strange Quark Matter in <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Theory of Gravity

We studied plane symmetric cosmological model in the presence of quark and strange quark matter with the help of f(R, T) theory. To decipher solutions of plane symmetric space-time, we used power law relation between scale factor and deceleration parameter. We considered the special law of variation of Hubble’s parameter proposed by Berman (Nuovo Cimento B74, 182, 1983) which yields constant deceleration parameter. We also discussed the physical behavior of the solutions by using some physical parameters.     

On some magnetohydrostatic similarity solutions

It is shown that some recently constructed similarity solutions in force-free configurations belong to a wider class of magnetohydrostatic equilibria, which allows more flexibility in the selection of the parameters of problems. For limiting configurations, solutions are constructed analytically, by means of matched asymptotic expansions, to a second-order approximation.     

Stability analysis for non-minimally coupled dark energy models in the Palatini formalism

In this paper, we use the method of global analysis to study the stability of de-Sitter solutions in an universe dominated by a scalar field dark energy, which couples non-minimally with the Ricci scalar defined in the Palatini formalism. Effective potential and phase-space diagrams are introduced to describe qualitatively the de-Sitter solutions and their stabilities. We find that for the simple power-law function \(V(\varphi)=V_{0}\varphi^{n}\) there are no stable de-Sitter solutions. While for some more complicated potentials, i.e. \(V(\varphi)=V_{0}\varphi^{n}+\varLambda\) and \(V(\varphi)=V_{0} (e ^{-\lambda\varphi}+e^{\lambda\varphi})^{2}\), stable de-Sitter solutions can exist.     

F and G Taylor series solutions to the Stark and Kepler problems with Sundman transformations

The classic $F$ and $G$ Taylor series of Keplerian motion are extended to solve the Stark problem and to use the generalized Sundman transformation. Exact recursion formulas for the series coefficients are derived, and the method is implemented to high order via a symbolic manipulator. The results lead to fast and accurate propagation models with efficient discretizations. The new $F$ and $G$ Stark series solutions are compared to the Modern Taylor Series (MTS) and 8th order Runge–Kutta–Fehlberg (RKF8) solutions. In terms of runtime, the $F$ and $G$ approach is shown to compare favorably to the MTS method up to order 20, and both Taylor series methods enjoy approximate order of magnitude speedups compared to RKF8 implementations. Actual runtime is shown to vary with eccentricity, perturbation size, prescribed accuracy, and the Sundman power law. The method and results are valid for both the Stark and the Kepler problems. The effects of the generalized Sundman transformation on the accuracy of the propagation are analyzed. The Taylor series solutions are shown to be exceptionally efficient when the unity power law from the classic Sundman transformation is applied. An example low-thrust trajectory propagation demonstrates the utility of the $F$ and $G$ Stark series solutions.     

Exact-Brans-Dicke-Friedmann-Robertson-Walker-Bianchi-Kantowski-Sachs vacuum solutions

Using a new method of reduction of the Brans-Dicke vacuum field equations we derive exact vacuum solutions for the class of spatially homogeneous space-times in a unified manner. Exact solutions are given for the isotropic Friedmann-Robertson-Walker models as well as for the anisotropic Bianchi types I-IX and for the related Kantowski-Sachs model.     

Cosmological solution with an energy flux

The paper presents some spherically symmetric cosmological Solutions in which the velocity field is shear-free but there is a flux of energy. The solutions are believed to be new and the previous known solutions of this class due to Bergmann and Maiti may be obtained as special cases of our metrics.     

A new shock locus for similarity solutions in one-dimensional unsteady gas dynamics

This paper deals with shock conditions for the progressing wave (or similarity) solutions of one-dimensional, unsteady gas dynamics. These solutions have hitherto been used to deal with the flow behind shocks moving into stationary atmospheres. By generalising the shock conditions to the case of moving atmospheres, it is shown that the progressing wave solutions can be used to describe a certain class of flows, and a new shock locus can be constructed in the phase plane of the solutions. It is hoped that such solutions will be of use in describing the unsteady flow behind shocks propagating into the ambient solar wind.