Regularity condition on the anisotropy induced by gravitational decoupling in the framework of MGD

Abstract

We use gravitational decoupling to establish a connection between the minimal geometric deformation approach and the standard method for obtaining anisotropic fluid solutions. Motivated by the relations that appear in the framework of minimal geometric deformation, we give an anisotropy factor that allows us to solve the quasi--Einstein equations associated to the decoupler sector. We illustrate this by building an anisotropic extension of the well known Tolman IV solution, providing in this way an exact and physically acceptable solution that represents the behavior of compact objects. We show that, in this way, it is not necessary to use the usual mimic constraint conditions. Our solution is free from physical and geometrical singularities, as expected. We have presented the main physical characteristics of our solution both analytically and graphically and verified the viability of the solution obtained by studying the usual criteria of physical acceptability.

9 pages, 10 figures. arXiv admin note: text overlap with arXiv:1908.08194

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Cited by in corpus (3)

• Stability of the isotropic pressure condition
• Gravitational decoupling for axially symmetric systems and rotating black holes
• Anisotropic 2+1 dimensional black holes by gravitational decoupling