Class Of Interior Solutions Research Articles

Modelling a new class of anisotropic compact stars satisfying the Karmakar’s condition

The present paper provides a new class of interior solutions which satisfies the Karmakar condition (K.R. Karmarkar, Proc. Indian Acad. Sci. A 27, 56 (1948)). The model is generated by assuming a reasonable choice for the metric potential $ g_{rr}$ and the model parameters are obtained accordingly since, in the case of embedding class-I, the metric co-efficients are dependent on each other. We match our interior solution to the exterior Schwarzschild line element in the presence of thin shell. The proposed model does not suffer from central singularity. The model is discussed for a neutron star of mass $ 1.4 M_{\odot}$ and radius 10km. The potential stability condition of the model is also discussed.

Finch-Skea star in $$(2+1)$$ dimensions

The Bañados et al. (Phys Rev Lett 69:1849, 1992) solution corresponding to the exterior space-time of a black hole in \((2+1)\) dimensions has been found to be very useful to understand various aspects relating to the gravitational field of a black hole. We present here a class of interior solutions corresponding to the BTZ exterior by making use of a model presented by Finch and Skea (Class Quantum Grav 6:467, 1989) which was earlier found to be relevant for the description realistic stars in \((3+1)\) dimensions. We show physical viability of the model in lower dimensions as well.

New class of well behaved exact Solutions for static charged Neutron-star with perfect fluid

The paper presents a class of interior solutions of Einstein–Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged fluid. This class of solutions describes well behaved charged fluid balls. This solution gives us wide range of parameter K (0.53≤K≤0.95), for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρb=2×1014 g/cm3. Corresponding to K=0.95 with X=−0.15, the maximum mass of the star comes out to be M=1.56 MΘ with radius rb≈9.22 km and the surface red shift Zb≈0.124207. It has been observed that under well behaved conditions this class of solutions gives us the mass of super dense object within the range of neutron star. However, its neutral counter part is not well behaved.

A class of interior solutions corresponding to a [formula omitted]-dimensional asymptotically anti-de Sitter spacetime

Lower-dimensional gravity has the potential of providing non-trivial and valuable insight into some of the conceptual issues arising in four-dimensional relativistic gravitational analysis. The asymptotically anti-de Sitter ( 2 + 1 )-dimensional spacetime described by Bañados, Teitelboim and Zanelli (BTZ) which admits a black hole solution, has become a source of fascination for theoretical physicists in recent years. By suitably choosing the form of the mass function m ( r ) , we derive a new class of solutions for the interior of an isotropic star corresponding to the exterior ( 2 + 1 ) asymptotically anti-de Sitter BTZ spacetime. The solution obtained satisfies all the regularity conditions and its simple analytical form helps us to study the physical parameters of the configuration in a simple manner.

New class of Well behaved exact solutions of relativistic charged white-dwarf star with perfect fluid

The paper presents a class of interior solutions of Einstein-Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid. This class of solutions describes well behaved charged fluid balls. The class of solutions gives us wide range of parameter K (0.3277≤K≤0.49), for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρb=2×1014 g/cm3. Corresponding to K=0.3277 with X=−0.15, the maximum mass of the star comes out to be M=0.92MΘ with radius rb≈17.15 km and the surface red shift Zb≈0.087187. It has been observed that under well behaved conditions this class of solutions gives us the mass of super dense object within the range of white-dwarf.

Fluid spheres and R- and T-regions in general relativity

R- and T-regions of spacetime are first defined in a particular coordinate system and then with the aid of the Schwarzschild vacuum solution are shown to represent the outside and inside of a black hole respectively. A certain class of interior solutions, relating to a perfect fluid, are also considered and it is found that these R- and T-solutions have distinct physical properties. The R-solutions are static, spherically symmetric, permanent, and have a classical analogue, while the corresponding T-solutions, which are wholly time dependent, are cylindrical, temporary, and do not have a classical analogue. It is shown that these T-solutions cannot be generated from their R-region counterparts. Particular T-solutions are also presented in which the corresponding fluid occupies the whole of a T-region. The fluid would under certain circumstances be black body radiation while for other cases the internal pressure is always greater than the density.

Postulational approach to schwarzschild’s exterior solution with application to a class of interior solutions

In order to clarify the physical ideas underlying Schwarzschild’s exterior solution, a postulational derivation is given that does not make use of the field equations. Basically this amounts to replacing two field equations by two postulates, one of which is a strong version of the principle of equivalence and the other, Newton’s inverse square law. These postulates are more general than the approach would indicate and there is actually a class of solutions for static systems with spherical symmetry which satisfy them. The energy-stress tensors producing these solutions have the important property that energy density equals radial stress. Two examples of interior solutions that fulfill these postulates are given: a solid sphere and a hollow shell. The basic properties of these solutions are described and compared with those of Schwarzschild’s interior solution. The solid sphere solution is used to complete a previous discussion of the clock paradox. In an Appendix, the field equations for static systems with spherical symmetry are written in a form that indicates the limitations of the postulates.