Abstract
In this article, we have proposed a model for a realistic strange star under Tolman VII metric\citep{Tolman1939}. Here the field equations are reduced to a system of three algebraic equations for anisotropic pressure. Mass, central density and surface density of strange star in the low-mass X-ray binary 4U 1820-30 has been matched with the observational data according to our model. Strange materials clearly satisfies the stability condition (i.e. sound velocities < 1) and TOV-equation. Here also surface red shift of the star has been found to be within reasonable limit.
Highlights
In 1939, Tolman [17] proposed static solutions for a sphere of fluid
In this work we have investigated the nature of anisotropic strange stars in the case of the low-mass X-ray binary 4U 1820-30 by making the following considerations: (a) The stars are anisotropic in nature i.e. pr = pt . (b) The spacetime of the strange stars can be described by the Tolman VII metric
At the centre of the star, its anisotropic behaviour vanishes. (ii) Our model is well stable according to the Herrera stability condition [14]. (iii) From the mass–radius relation, any interior features of the star can be evaluated
Summary
In 1939, Tolman [17] proposed static solutions for a sphere of fluid. In that article, he pointed out that due to the complexity of the VIIth solution (among the eight different solutions), it is not a feasible one for physical consideration [there was a misprint in the Tolman solution VII (4.7) but that does not affect the original solution]. We consider that the interior spacetime geometry of the strange star is Tolman VII type and try to investigate the matter distributions which produce this spacetime. Our calculations show that the matter distribution that produces a Tolman VII type spacetime geometry should be anisotropic. This helps us in modelling the strange star which is anisotropic in nature as the density within the strange stars is normally beyond the nuclear matter density. We choose the interior spacetime geometry of the strange star to be Tolman VII type and try to investigate the matter distributions which produce this spacetime. 3, we study the physical behaviours of the star, namely, anisotropic behaviour, matching conditions, TOV equations, energy conditions, stability and mass–radius relation and surface redshift in different sub-sections.
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