In this article, we attempt to find a singularity free solution of Einstein's field equations for compact stellar objects, precisely strange (quark) stars, considering Schwarzschild metric as the exterior spacetime. To this end, we consider that the stellar object is spherically symmetric, static and anisotropic in nature and follows the density profile given by Mak and Harko (2002), which satisfies all the physical conditions. To investigate different properties of the ultra-dense strange stars we have employed the MIT bag model for the quark matter. Our investigation displays an interesting feature that the anisotropy of compact stars increases with the radial coordinate and attains Preprint submitted to Annals of Physics October 19, 2017 its maximum value at the surface which seems an inherent property for the singularity free anisotropic compact stellar objects. In this connection we also perform several tests for physical features of the proposed model and show that these are reasonably acceptable within certain range. Further, we find that the model is consistent with the energy conditions and the compact stellar structure is stable with the validity of the TOV equation and Herrera cracking concept. For the masses bellow the maximum mass point in mass vs radius curve the typical behavior achieved within the framework of general relativity. We have calculated the maximum mass and radius of the strange stars for the three finite values of bag constant B g .
In the present investigation an exact generalised model for anisotropic compact stars of embedding class 1 is sought with a general relativistic background. The generic solutions are verified by exploring different physical aspects, viz. energy conditions, mass-radius relation, stability of the models, in connection to their validity. It is observed that the model presented here for compact stars is compatible with all these physical tests and thus physically acceptable as far as the compact star candidates R X J 1856-37, S AX J 1808.4-3658 (SS1) and S AX J 1808.4-3658 (SS2) are concerned.
In this article we try to present spherically symmetric isotropic strange star model under the framework of f(R,𝒯) theory of gravity. To this end, we consider that the Lagrangian density is a linear function of the Ricci scalar R and the trace of the energy momentum tensor 𝒯 given as f(R,𝒯)=R+2χ 𝒯. We also assume that the quark matter distribution is governed by the simplest form of the MIT bag model equation of state (EOS) as p=1/3(ρ−4B), where B is the bag constant. We have obtained an exact solution of the modified form of the Tolman-Oppenheimer-Volkoff (TOV) equation in the framework of f(R,𝒯) gravity theory and have studied the dependence of different physical properties, viz., the total mass, radius, energy density and pressure for the chosen values of χ. Further, to examine physical acceptability of the proposed stellar model, we have conducted different tests in detail, viz., the energy conditions, modified TOV equation, mass-radius relation, causality condition etc. We have precisely explained the effects arising due to the coupling of the matter and geometry on the compact stellar system. For a chosen value of the bag constant, we have predicted numerical values of the different physical parameters in tabular form for the different strange star candidates. It is found that as the factor χ decreases the strange star candidates become gradually massive and larger in size with less dense stellar configuration. However, when χ increases the stars shrink gradually and become less massive to turn into a more compact stellar system. Hence for χ>0 our proposed model is suitable to explain the ultra-dense compact stars well within the observational limits and for χ<0 case allows to represent the recent massive pulsars and super-Chandrasekhar stars. For χ=0 we retrieve as usual the standard results of the general relativity (GR).
The present work is focused on the investigation of the existence of compact structures describing anisotropic matter distributions within the framework of modified gravity theories, specifically f(R,T ) gravity theory. Additionally, we have taken f(R,T ) as a linear function of the Ricci scalar R and the trace of the energy-momentum tensor T as f (R, T )=R + 2χT ,where χ is a dimensionless coupling parameter, and the Lagrangian matter Lm = − 1 3 (2pt + pr), to describe the complete set of field equations for the anisotropic matter distribution. We follow the embedding class one procedure using Eisland condition to obtain a full space-time description inside the stellar configuration. Once the space-time geometry is specified we determine the complete solution of modified Einstein equations by using the MIT bag model equation of state pr = 1 3 (ρ − 4B) that describes the strange quark matter (SQM) distribution inside the stellar system, where B denotes a bag constant. The physical validity of our anisotropic solution is confirmed by executing several physical tests. It is worth mentioning that with the help of the observed mass values for the various strange star candidates we have predicted the exact radii by taking different values for χ and B. These predicted radii show monotonic decreasing nature as the parameter χ is moved from −0.8 to 0.8 progressively. In this case, our anisotropic stellar system becomes more massive and transforms into more dense compact stars. We also performed a detailed graphical analysis of the compact star. As a result, for χ < 0, the current modified f (R, T ) gravity seems promising to explain the observed massive compact astrophysical objects, similar to magnetars, massive pulsars, and Chandrasekhar super white dwarfs, which is not justified in the framework of general relativity. Finally, note that when χ = 0 general relativity results for anisotropic matter distributions are recovered.
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