Diverse regular spacetimes using a parametrised density profile

Abstract: We explore the construction of diverse regular spacetimes (black holes and defects) in General Relativity (GR) using a generic parametrised density profile (the Dekel-Zhao profile), which includes, for specific parameter choices, various well-known examples usually studied in the context of dark matter halos. Our solutions, in the Schwarzschild gauge, include new regular black holes as well as non-singular solutions representing spacetime defects. For a sub-class of metrics, a TOV equation approach with a chosen equation of state works. The status of the energy conditions and the issue of geodesic completeness are explored in detail. We also provide possible Lagrangian density constructions for the matter energy-momentum tensors. Further, we study the shadow radius of the new regular black holes, and compare our findings with available observational results from the EHT collaboration. Finally, for the defect solution, we present a model for a stable star (a gravastar) by explicit use of the junction conditions and obtain relevant consequences highlighting its characteristic features.