Self-consistent and stable stellar structures in massive gravity

In this investigation, we introduce a novel generic class of stellar configurations within the framework of de Rham–Gabadadze–Tolley massive gravity (dRGT), which aligns well with empirical observational data. The geometric structure analyzed is characterized by static and spherically symmetric properties and incorporates an anisotropic matter distribution. The governing Einstein field equations are adeptly resolved by employing the Durgapal–Lake (DL) metric potentials. The unknown constants are integral to these potentials, with their respective values determined through a comparative analysis with the Schwarzschild line-element, serving as an external geometry at the stellar surface corresponding to the interior space–time. Our comprehensive evaluation of this proposed model affirms its viability as a physically consistent compact object within the dRGT paradigm. This analysis encompasses a diverse array of compact star candidates, representing a broader category of compact stellar structures. The findings reveal that the model exhibits stable characteristics devoid of singularities while effectively encapsulating a wide spectrum of observed compact objects in astrophysical scenarios. This rigorous assessment ensures adherence to essential physical criteria, thereby enhancing its relevance in elucidating the dynamics of compact stars.