A realistic stellar model based on an ansatz of Duorah and Ray

Abstract

It is shown that the analytical stellar model of Duorah and Ray (1987) does not satisfy Einstein's field equations. All possible solutions derivable from the generalised density distribution are exhibited; these include a solution due to Durgapal and Bannerji. The correct solution following from the ansatz of Duorah and Ray is given. The equation of state for the model is obtained in terms of elementary functions, and the solution is shown to be both regular and physically realistic for a range of masses and radii. A comparison between the model and numerical integrations of neutron stars described by Walecka's relativistic mean-field theory description of neutron matter shows good overall agreement.

Anisotropic extension of Finch and Skea stellar model

“…The spacetime geometry of Finch and Skea (1989), originally developed by Duorah and Ray (1987), has got much attention in the modelling of relativistic compact stars as the solution is well-behaved and satisfies all criteria of physical acceptability (Delgaty and Lake (1998)). The Finch-Skea isotropic stellar model has subsequently been generalized by many investigators to study a large variety of stellar bodies by incorporating electro-magnetic field and anisotropic pressure.…”

Modified Finch and Skea stellar model compatible with observational data

“…1 Introduction Finch and Skea (1989), making use of Duorah and Ray (1987) ansatz for the metric potential g rr corresponding to a static spherically symmetric perfect fluid spacetime, developed a stellar model which was later shown to comply with all the physical requirements of a realistic star by Delgaty and Lake (1998). Consequently, the Finch-Skea model has been explored by many investigators in different astrophysical contexts, particularly for the studies of cold compact stellar objects (see for example, Hansraj and Maharaj (2006); Tikekar and Jotania (2009) ;Banerjee et al (2013)).…”

“…Consequently, the Finch-Skea model has been explored by many investigators in different astrophysical contexts, particularly for the studies of cold compact stellar objects (see for example, Hansraj and Maharaj (2006); Tikekar and Jotania (2009) ;Banerjee et al (2013)). One noticeable feature of the Finch and Skea (1989) model is that it assumes isotropy in pressure. However, theoretical investigations of Ruderman (1972) and Canuto (1974), amongst others have shown that anisotropy might develop in the high density regime of compact stellar objects.…”

“…In this paper, we have generalized the Sharma and Ratanpal (2013) model by incorporating a dimensionless parameter n(> 0) in the Finch and Skea (1989) ansatz and assumed the system to be anisotropic, in general. We have shown that such assumptions can provide physically viable solutions which can be used to model realistic stars.…”

“…In particular, we have shown that the predicted masses and radii of pulsars like 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, PSR J1614-2230, SAX J1808.4-3658 and Her X-1 can well be achieved by systematically fixing the parameter n. Most importantly, for a given mass, it is possible to constrain the radius so as to get the desired compactness by fixing the compactness parameter n in this model. The paper has been organized follows: In 2, for a static spherically symmetric anisotropic fluid sphere, we have solved the relevant field equations by making a particular choice of the metric potential g rr which is a generalization of the Finch and Skea (1989) ansatz. In 3, we have laid down the boundary conditions and in 4, we have put constraints on the model parameters based on physical requirements, regularity conditions and stability.…”