Multi-Layered Static Dense stars in Einstein's Gravity: Applications of general relativity modelling compact

This monograph presents a rigorous analysis of multilayered compact stars within Einstein's gravitational framework, extending beyond isotropic fluid models to incorporate pressure anisotropy, stratified interiors with exotic phases, and baryonic-dark energy coupling, thereby achieving a physically faithful description of supra-nuclear matter.Exact solutions of non-linear field equations are constructed using Tolman-Kuchowicz, Vaidya-Tikekar, Buchdahl-I, and biquadratic geometries, with physical admissibility ensured via Darmois-Israel matching conditions. Stability is systematically examined through the generalized Tolman-Oppenheimer-Volkoff equilibrium, causality bounds, energy conditions, and cracking criteria.Four observationally grounded configurations are developed: dark energy-admixed stars exhibiting enhanced stability and higher mass limits; Karmarkar-constrained models consistent with massive pulsars; a three-layered quark-condensate-neutron structure motivated by phase transitions; and a two-layered core-shell system revealing mesonic interface dynamics.