Modeling and stability analysis of compact objects in f(G) gravity

This study investigates compact anisotropic stellar structures using the class-1 embedding technique within the framework of modified Gauss-Bonnet gravity (i.e. f(G)). A short review of the theory is presented and the field equations are formulated by considering the well-studied model, f(G)=αGm, where m and α are positive constants. Furthermore, we utilize the Karmarkar condition to establish a connection between the metric potentials grr and gtt. By adopting a specific model for one of the metric potentials, we derive the second potential through the application of the Karmarkar condition. The research focuses on determining unknown constants by matching the interior space-time of these stellar models with the exterior Schwarzschild geometry. By applying the observational data of some compact star candidates such as XTEJ1739−217, HerX−1, 4U153852, 4U1608−52 and CenX−3, the study provides a rigorous analysis of the proposed model in terms of stability and physical viability through the evolution of energy constraints, cracking constraints, adiabatic index, evolution of mass function and compactness, and the hydrostatic equilibrium of forces applied on the system and confirmed that our presented model is suitable to investigate the complex interior configuration of stellar structures.