Abstract
In this work we have extended the Maurya-Gupta isotropic fluid solution to Einstein field equations to an aniso-tropic domain. To do so, we have employed the gravitational decoupling via the minimal geometric deformation approach. The present model is representing the strange star candidate LMC X-4. A mathematical, physical and graphical analysis, shown that the obtained model fulfills all the criteria to be an admissible solution of the Einstein field equations. Specifically, we have analyzed the regularity of the metric potentials and the effective density, radial and tangential pressures within the object, causality condition, energy conditions, equilibrium via Tolman–Oppenheimer–Volkoff equation and the stability of the model by means of the adiabatic index and the square of subliminal sound speeds.
Highlights
Tnm = Tnm + βθnm, (1)where Tnm represents a perfect fluid matter distribution and θnm is the extra source which encodes the anisotropy and can be formed by scalar, vector or tensor fields
Over the last decade a lot of works available in the literature have considering the inclusion of anisotropic matter distribution in solving analytical models to Einstein field equations [69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109](and references contained therein)
For this purpose we will use the Israel–Darmois junction conditions [118,119]. These conditions require the continuity of the metric potentials eν(r) and eλ(r) across the surface Σ of the compact object defined by r = R (It is known as the first fundamental form)
Summary
Where Tnm represents a perfect fluid matter distribution and θnm is the extra source which encodes the anisotropy and can be formed by scalar, vector or tensor fields. Theoretical researches in the past developed by Ruderman [29] Canuto [30,31,32] and Canuto et al [33,34,35,36] revealed that anisotropies can be emerged when matter density is higher than the nuclear density one. The presence of anisotropy introduces several and novel features in the matter distribution, e.g. in presence of a positive anisotropy factor Δ ≡ pt − pr > 0, the stellar configuration experiences a repulsive force (attractive in the case of negative anisotropy factor) that offsets the gravitational gradient
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