We present a new systematic approach to find the exact gravitationally decoupled anisotropic spherical solution in the presence of electric charge by using the complete geometric deformation (CGD) methodology. To do this, we apply the transformations over both gravitational potentials by introducing two unknown deformation functions. This new systematic approach allows us to obtain the exact solution of the field equations without imposing any particular ansatz for the deformation functions. Specifically, a well-known mimic approach and equation of state (EOS) have been applied together for solving the system of equations, which determine the radial and temporal deformation functions, respectively. The matching conditions at the boundary of the stellar objects with the exterior Reissner–Nordström metric are discussed in detail. In order to see the physical validity of the solution, we used well-behaved interior seed spacetime geometry and solved the system of equations using the above approaches. Next, we presented several physical properties of the solution through their graphical representations. The stability and dynamical equilibrium of the solution have been also discussed. Finally, we predicted the radii and mass-radius ratio for several compact objects for different decoupling parameters together with the impact of the decoupling parameters on the thermodynamical observables.

In this article, we develop a theoretical framework to study compact stars in Einstein gravity with the Gauss–Bonnet (GB) combination of quadratic curvature terms. We mainly analyzed the dependence of the physical properties of these compact stars on the Gauss–Bonnet coupling strength. This work is motivated by the relations that appear in the framework of the minimal geometric deformation approach to gravitational decoupling (MGD-decoupling), we establish an exact anisotropic version of the interior solution in Einstein–Gauss–Bonnet gravity. In fact, we specify a particular form for gravitational potentials in the MGD approach that helps us to determine the decoupling sector completely and ensure regularity in interior space-time. The interior solutions have been (smoothly) joined with the Boulware–Deser exterior solution for 5D space-time. In particular, two different solutions have been reported which comply with the physically acceptable criteria: one is the mimic constraint for the pressure and the other approach is the mimic constraint for density. We present our solution both analytically and graphically in detail.

In this work, we present a hierarchical solution-generating technique employing the Minimum Gravitational Decoupling (MGD) Method and the generalized concept of Complexity as applied to Class I spacetime for bounded compact objects in classical general relativity. Starting off with an anisotropic seed solution described by Class I spacetime, we apply the MGD technique with the constraint that the effective anisotropy vanishes which leads to an isotropic model. In addition, we produce a second family of solutions in which the Complexity factor [Herrera (Phys Rev D 97:044010, 2018)] for the seed solution and its MGD counterpart are the same. We discuss the physical plausibility of both classes of solutions as candidates for physically realizable compact objects.

In this paper, we study novel classes of solutions characterizing the role of complexity on static and spherically symmetric self‐gravitating systems proposed by L. Herrera (Phys Rev D 97: 044010, 2018) in the gravitational decoupling background. We start by considering the minimal geometric deformation approach as a ground‐breaking tool for generating new physically viable models for anisotropic matter distributions by exploiting the Buchdahl and Tolman models. In both models, all solutions show similar results with a slight change in their magnitude for a non‐vanishing complexity factor i.e., , where β is a decoupling constant. However, under vanishing complexity factor i.e., , the minimally deformed anisotropic Buchdahl model yielded a constant density isotropic fluid distribution and anisotropic matter distribution becomes an isotropic fluid matter distribution without invoking any isotropy requirement. On the other hand, Tolman model possesses an increasing pressure when the complexity factor vanishes. Furthermore, we also extend our findings by calculating the mass‐complexity factor relationship for both presented models, revealing that the mass is larger for small values of the decoupling constant β and the complexity factor .

In the present paper, we discuss the role of gravitational decoupling to isotropize the anisotropic solution of Einstein’s field equations in the context of the complete geometric deformation (CGD) approach and its influence on the complexity factor introduced by Herrera (Phys Rev D 97:044010, 2018) in the static self-gravitating system. Moreover, we proposed a simple and effective technique as well to generate new solutions for self-gravitating objects via CGD approach by using two systems with the same complexity factor and vanishing complexity factor proposed by Casadio et al. (Eur Phys J C 79:826, 2019). The effect of decoupling constant and the compactness on the complexity factor have also been analyzed for the obtained solutions.