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Regular decoupling sector and exterior solutions in the context of MGD

Abstract:

We implement the gravitational decoupling through the minimal geometric deformation method and explore its effect on exterior solutions by imposing a regularity condition in the Tolman-Oppenheimer-Volkoff equation of the decoupling sector. We obtain that the decoupling function can be expressed formally in terms of an integral involving the g tt component of the metric of the seed solution. As a particular example, we implement the method by using the Schwarzschild exterior as a seed and we obtain that the asymptotic behavior of the extended geometry corresponds to a manifold with constant curvature.