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Journal ArticleDOI

Exact Relativistic Model for a Superdense Star

01 Sep 1982-Journal of Astrophysics and Astronomy (Springer India)-Vol. 3, Iss: 3, pp 325-334
TL;DR: In this article, a static spherically symmetric model based on an exact solution of Einstein's equations is given which will permit densities of the order of 2 × 1014 gm cm-3, radii of a few kilometers and masses up to about four times the solar mass.
Abstract: Assuming that the physical 3-spacet = const in a superdense star is spheroidal, a static spherically symmetric model based on an exact solution of Einstein’s equations is given which will permit densities of the order of 2 × 1014 gm cm-3, radii of the order of a few kilometers and masses up to about four times the solar mass.
Citations
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Journal ArticleDOI
TL;DR: In this paper, interior perfect fluid solutions for the Reissner-nordstrom metric are studied on the basis of a new classification scheme, which specifies which two of the characteristics of the fluid are given functions and accordingly picks up one of the three main field equations, the other two being universal.
Abstract: Interior perfect fluid solutions for the Reissner-Nordstr\"om metric are studied on the basis of a new classification scheme. It specifies which two of the characteristics of the fluid are given functions and accordingly picks up one of the three main field equations, the other two being universal. General formulas are found for charged de Sitter solutions, the case of a constant energy component of the energy-momentum tensor, the case of known pressure (including charged dust), and the case of a linear equation of state. Explicit new global solutions, mainly in elementary functions, are given as illustrations. The known solutions are briefly reviewed and corrected.

311 citations

Journal ArticleDOI
TL;DR: In this paper, a class of solutions to the Einstein-Maxwell system for a charged sphere with a particular choice of the electric field intensity was proposed, and a qualitative analysis of the physical features of the model was performed.
Abstract: We find a class of solutions to the Einstein–Maxwell system for a charged sphere with a particular choice of the electric field intensity by assuming a particular form for the hypersurfaces {t = constant}. In the uncharged limit we regain static stars studied previously. A qualitative analysis of the physical features of the model is performed. The presence of charge allows for more general behaviour than is the case for uncharged spheres. In particular we show that the causal signals are permitted over a wider range of parameters in the presence of charge. Also we show that our solutions satisfy a simple scaling relationship.

183 citations

Journal ArticleDOI
P. S. Negi1
TL;DR: In this article, it is shown that the exterior Schwarzschild solution itself provides necessary conditions for the types of the density distributions to be considered inside the mass, in order to obtain exact solutions or equations of state compatible with the state of hydrostatic equilibrium in general relativity.
Abstract: We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in Negi and Durgapal [Gravitation and Cosmology 7, 37 (2001)] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic equilibrium. It is seen that this criterion is fulfilled only by (i) the regular solutions having a vanishing surface density together with pressure, and (ii) the singular solutions corresponding to a non-vanishing density at the surface of the configuration. On the other hand, the regular solutions corresponding to a non-vanishing surface density do not fulfill this criterion. Based upon this investigation, we point out that the exterior Schwarzschild solution itself provides necessary conditions for the types of the density distributions to be considered inside the mass, in order to obtain exact solutions or equations of state compatible with the state of hydrostatic equilibrium in general relativity. The regular solutions with finite centre and non-zero surface densities which do not fulfill the criterion given by Negi and Durgapal (2001), in fact, cannot meet the requirement of the‘actual mass’, set up by exterior Schwarzschild solution. The only regular solution which could be possible in this regard is represented by uniform (homogeneous) density distribution. This criterion provides a necessary and sufficient condition for any static and spherical configuration (including core-envelope models) to be compatible with the structure of general relativity [that is, the state of hydrostatic equilibrium in general relativity]. Thus, it may find application to construct the appropriate core-envelope models of stellar objects like neutron stars and may be used to test various equations of state for dense nuclear matter and the models of relativistic star clusters with arbitrary large central redshifts.

177 citations

Journal ArticleDOI
TL;DR: In this article, a static spherically symmetric model based on an analytic closed-form solution of Einstein's field equations is presented, assuming the density of the order of 2×1014 g/cm−3.
Abstract: Assuming that the physical three‐space in a relativistic superdense star has the geometry of a three‐spheroid, a static spherically symmetric model based on an analytic closed‐form solution of Einstein’s field equations is presented. Assuming the density of the order of 2×1014 g cm−3, estimates of the total mass and size of the stars of the model are obtained for various values of a density‐variation parameter that is suitably defined. The total mass and the boundary radius of each of these models are of the order of the mass and size of a neutron star.

129 citations

Journal ArticleDOI
TL;DR: In this paper, the authors presented a class of relativistic solutions describing spherically symmetric and static anisotropic stars in hydrostatic equilibrium, including the Vaidya-Tikekar and Finch-Skea solutions.
Abstract: In this article we present a class of relativistic solutions describing spherically symmetric and static anisotropic stars in hydrostatic equilibrium. For this purpose, we consider a particularized metric potential, namely, Buchdahl ansatz [Phys. Rev. D 116, 1027 (1959).] which encompasses almost all the known analytic solutions to the spherically symmetric, static Einstein equations with a perfect fluid source, including, in particular, the Vaidya-Tikekar and Finch-Skea. We developed the model by considering an anisotropic spherically symmetric static general relativistic configuration that has a significant effect on the structure and properties of stellar objects. We have considered eight different cases for generalized Buchdahl dimensionless parameter $K$ and analyzed them in a uniform manner. As a result it turns out that all the considered cases are valid at every point in the interior spacetime. In addition to this, we show that the model satisfies all the energy conditions and maintains the hydrostatic equilibrium equation. In the frame work of anisotropic hypothesis, we consider analogue objects with similar mass and radii, such as LMC X-4, SMC X-1, EXO 1785-248 etc. to restrict the model parameter arbitrariness. Also, establishing a relation between pressure and density in the form of $P=P(\ensuremath{\rho})$, we demonstrate that equation of state (EoS) can be approximated to a linear function of density. Despite the simplicity of this model, the obtained results are satisfactory.

109 citations

References
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Journal ArticleDOI
TL;DR: In this article, a method is developed for treating Einstein's field equations, applied to static spheres of fluid, in such a manner as to provide explicit solutions in terms of known analytic functions.
Abstract: A method is developed for treating Einstein's field equations, applied to static spheres of fluid, in such a manner as to provide explicit solutions in terms of known analytic functions. A number of new solutions are thus obtained, and the properties of three of the new solutions are examined in detail. It is hoped that the investigation may be of some help in connection with studies of stellar structure. (See the accompanying article by Professor Oppenheimer and Mr. Volkoff.)

2,264 citations

Journal ArticleDOI
TL;DR: On the basis of the theory of relativity, the principle of causality, and Le Chatelier's principle, it was shown in this article that the maximum mass of the equilibrium configuration of a neutron star cannot be larger than $3.2{M}_{[m?]}
Abstract: On the basis of Einstein's theory of relativity, the principle of causality, and Le Chatelier's principle, it is here established that the maximum mass of the equilibrium configuration of a neutron star cannot be larger than $3.2{M}_{[m?]}$. The extremal principle given here applies as well when the equation of state of matter is unknown in a limited range of densities. The absolute maximum mass of a neutron star provides a decisive method of observationally distinguishing neutron stars from black holes.

546 citations