Class I approach as MGD generator

Abstract In this work we build a relativistic anisotropic admissible compact structures. To do so we combine the class I approach with gravitational decoupling in order to generate the deformation function f ( r ). As an example we have re-anisotropized two anisotropic matter distributions previously obtained by the class I procedure. To produce all the graphical study supporting this analysis, we have considered the data corresponding to the compact object 4U 1538-52, SMC X-1 and LMC X-4 for model 1 and Cen X-3 for model 2. In considering the last one, we have taken the constant parameter $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> to be $$\{-0.3;0.1;0.3\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>{</mml:mo><mml:mo>-</mml:mo><mml:mn>0.3</mml:mn><mml:mo>;</mml:mo><mml:mn>0.1</mml:mn><mml:mo>;</mml:mo><mml:mn>0.3</mml:mn><mml:mo>}</mml:mo></mml:mrow></mml:math> . It is found that the resulting models satisfy all the general requirement in order to represent or describe realistic compact structures such as neutron or quark stars.

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