Abstract
In this article, we develop a theoretical framework to study compact stars in Einstein gravity with the Gauss–Bonnet (GB) combination of quadratic curvature terms. We mainly analyzed the dependence of the physical properties of these compact stars on the Gauss–Bonnet coupling strength. This work is motivated by the relations that appear in the framework of the minimal geometric deformation approach to gravitational decoupling (MGD-decoupling), we establish an exact anisotropic version of the interior solution in Einstein–Gauss–Bonnet gravity. In fact, we specify a particular form for gravitational potentials in the MGD approach that helps us to determine the decoupling sector completely and ensure regularity in interior space-time. The interior solutions have been (smoothly) joined with the Boulware–Deser exterior solution for 5D space-time. In particular, two different solutions have been reported which comply with the physically acceptable criteria: one is the mimic constraint for the pressure and the other approach is the mimic constraint for density. We present our solution both analytically and graphically in detail.
Highlights
It turns out that apart from the first two terms corresponding to the Lovelock Lagrangian the third term is a combination of the second-order curvature term, namely Gauss–Bonnet (GB) [2]
Where the surface defined by r = R. This condition determines the object size. This is so because, the pressure decreases as we approach to the surface and the pressure at the exterior of the star must be null, this will correspond to the star boundary
Whereas in the same figures we see that the causality condition is satisfied for inclusion of β, which means compact stars obtained from the minimal geometric deformation (MGD) approach to gravitational decoupling satisfying the physically acceptable conditions
Summary
It turns out that apart from the first two terms corresponding to the Lovelock Lagrangian the third term is a combination of the second-order curvature term, namely Gauss–Bonnet (GB) [2]. In an attempt to generate exact solutions, the Minimal Geometric Deformation (MGD) was initially proposed in [52,53] to study the exterior geometry around spherically symmetric spacetime with a perfect fluid source in the framework of Randall–Sundrum brane-world gravity. This method was utilized by many researchers to generate and analyze physically viable models of astrophysical objects [54,55,56,57,58].
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