Abstract
We attempt to study a singularity-free model for the spherically symmetric anisotropic strange stars under Einstein’s general theory of relativity by exploiting the Tolman–Kuchowicz (Tolman in Phys Rev 55:364, 1939; Kuchowicz in Acta Phys Pol 33:541, 1968) metric. Further, we have assumed that the cosmological constant varLambda is a scalar variable dependent on the spatial coordinate r. To describe the strange star candidates we have considered that they are made of strange quark matter distribution, which is assumed to be governed by the MIT bag equation of state. To obtain unknown constants of the stellar system we match the interior Tolman–Kuchowicz metric to the exterior modified Schwarzschild metric with the cosmological constant, at the surface of the system. Following Deb et al. (Ann Phys 387:239, 2017) we have predicted the exact values of the radii for different strange star candidates based on the observed values of the masses of the stellar objects and the chosen parametric values of the varLambda as well as the bag constant {mathcal {B}}. The set of solutions satisfies all the physical requirements to represent strange stars. Interestingly, our study reveals that as the values of the varLambda and {mathcal {B}} increase the anisotropic system become gradually smaller in size turning the whole system into a more compact ultra-dense stellar object.
Highlights
In the aspect of Cosmology, the cosmological constant Λ as introduced by Einstein in general theory of relativity (GR) to match the Mach principle and to have a non-expanding static solution of the universe, becomes very significant
The erstwhile cosmological constant was conjectured as a constant quantity but gradually it appears that Λ is a scalar variable
We have considered an anisotropic fluid sphere in the framework of Einstein’s general theory of relativity
Summary
In the aspect of Cosmology, the cosmological constant Λ as introduced by Einstein in GR to match the Mach principle and to have a non-expanding static solution of the universe, becomes very significant. The basic ideas involved in the anisotropy and their applications in the diverse fields are available in the recent literature [3,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57] It is argued by Maurya [58] that the chances of having anisotropy is much higher in the compact stars because the interaction among the particles is highly relativistic and they become very random to maintain any uniform distribution throughout the region.
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