A new class of charged superdense star models is obtained by using an electric intensity, which involves two parameters, K and n. The metric describing the model shares its metric potential g44 with that of Durgapal's fourth solution.1 The pressure-free surface is kept at the density 2 × 1014 g/cm 3and joins smoothly the Reissner–Nordstrom solution. The neutral solution is well-behaved for 0 < Ca2 ≤ 0.2645, while its charge analogs are well-behaved for a wide range, 0 < K < 32, i.e. the pressure, density, pressure–density ratio and velocity of sound are monotonically decreasing and the electric intensity is monotonically increasing in nature for the given range of the parameter K. The maximum mass and the corresponding radius occupied by the neutral solution are 4.1826 MΘ and 19.7120 km, respectively for Ca2 = 0.2645, while the redshift at the center and at the surface are given by Z0 = 1.6444 and Za = 0.6538, respectively. For the charged solution, the maximum mass and radius are 6.3811MΘ and 19.1609 km, respectively for K = 1.4, n = 1 and Ca2 = 0.5016, with the redshift at the center Z0 = 3.7437 and at the surface Za = 1.1038.
First ever closed form solution for charged fluid sphere expressed by a space time with its hypersurfaces t = constant as spheroid is obtained for the case 0 < K < 1. The same is utilized to construct a superdense star with surface density 2×10 14 gm/cm 3 . The star is seen to satisfy the reality and causality conditions for 0 < K ≤ 0.045 and possesses maximum mass and radius to be 0.065216M and 1.137496 km respectively. Moreover the interior of the star satisfy strong energy condition. However in the absence of the causality condition, the reality conditions are valid for a wider range 0 < K ≤ 0.13. The maximum mass and radius for the later case are 1.296798M and 2.6107 km respectively for the strong energy condition, while the said parameters for the weak energy condition read as 1.546269M and 2.590062 km respectively.
.Two fluid-flow problems are solved using perturbation expansions, with special emphasis on the reduction of intermediate expression swell. This is done by developing tools in Maple that contribute to the efficient representation and manipulation of large expressions. The tools share a common basis, which is the creation of a hierarchy of representation levels such that expressions located at higher levels are expressed using entries from lower levels. The evaluation of higher-level expressions by the algebra system does not proceed recursively to the lowest level, as would ordinarily be the case, but instead can be directly controlled by the user.The first fluid-flow problem, arising in lubrication theory, is solved by implementing a technique of switch-controlled evaluation. The processes of simplification and evaluation are controlled at each level by user-manipulated switches. A perturbation solution is derived semi-interactively with the switch-controlled evaluation being used to reduce the size of intermediate expressions. The second fluid problem, in convection, is solved by extending a perturbation series in several variables to high order by implementing techniques for the automatic generation of hierarchical expression sequences.
In the present paper, nonconformal spherical symmetric perfect fluid solutions to Einstein field equations are obtained by using the invariance of the equations under the Lie group of transformations and some new solutions of this category are obtained satisfying the reality conditions like ρ ≥ p ≥ 0, ρr < 0, pr < 0 (p and ρ being pressure and energy-density respectively) in the region 0 < r < a. Such fluids do not represent isolated fluid spheres as pressure free interface is not possible for nonconformally perfect fluids of class one.
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