Abstract
In this work we investigate the extra packing of mass within the framework of gravitational decoupling by means of Minimal Geometric Deformation approach. It is shown that, after a suitable set of the free parameters involved, the like-Tolman IV solution extended by Minimal Geometric Deformation not only acquire extra packing of mass but it corresponds to a stable configuration according to the adiabatic index criteria. Additionally, it is shown that the extra packing condition induce a lower bound on the compactness parameter of the seed isotropic solution and a stringent restriction on the decoupling parameter.
Highlights
IntroductionIt is worth mentioning that in many applications of the gravitational decoupling (GD), Tμν is the source of a well known isotropic interior solution, so the effect of θμν is to introduce a local anisotropy in the system and it is said that GD leads to an extension of isotropic solutions to anisotropic domains
M/R ≤ 4/9 that corresponds to a maximum gravitational surface red-shift zs = 2.as pointed out by Ruderman in his pioneering work [3], celestial bodies are not necessarily made of isotropic matter but they could contain local anisotropies at least in certain very high density ranges (ρ > 1015 g/cm3), where the nuclear interactions must be treated relativistically
The celebrated article by Bowers and Liang [11] laid the initial basis for the study of anisotropic structures within the framework of Einstein’s general relativity (GR on). They found that the contributions coming from local anisotropies into the Tolman– Oppenheimer–Volkoff (TOV) equation [1,12] is of Newtonian origin
Summary
It is worth mentioning that in many applications of the GD, Tμν is the source of a well known isotropic interior solution, so the effect of θμν is to introduce a local anisotropy in the system and it is said that GD leads to an extension of isotropic solutions to anisotropic domains In this case, either the geometric deformation and the components of θμν remain unknown and the main goal is to provide suitable extra constraints which allow to find them. The modification of the Buchdahl limit in the framework of GD is straightforward, surprisingly it has not been considered yet to investigate the extra packing of mass of interior stellar For this reason, the main goal of this work is to employ the Bömer and Harko methodology in [50] to study the Buchdahl limit for anisotropic compact stars but assuming that the anisotropy is encoded in the θ -sector induced by the GD approach. Throughout the article we shall employ the mostly negative signature (+, −, −, −)
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