Relativistic models for vanishing complexity factor and isotropic star in embedding Class I spacetime using extended geometric deformation approach

Abstract In this work, we employ the Karmarkar condition together with the notion of vanishing complexity (Herrera in Phys Rev D 97:044010, 2018) and isotropization technique to generate models of compact stars within the framework of complete geometric deformation. Starting off with the Kuchowicz ansatz as one of the metric potentials for the seed solution, we impose the Karmarkar condition to obtain fully the gravitational behaviour of a static compact object with anisotropic pressure. This solution is then subjected to the complete geometric deformation algorithm. The novelty in our work is to impose the condition of vanishing complexity and isotropization techniques in order to derive the deformation functions. We present two solutions of the resulting governing equations which are subjected to physical viability tests. We demonstrate that the presence of pressure anisotropy within the bounded object plays a key role in determining its stability. In addition, we show that the magnitude of the decoupling constant determines the direction of energy flow between the generic fluid and the fluid matter distribution.