Construcción de un modelo estelar compacto en el espacio-tiempo de Buchdahl-Vaidya-Tikekar con complejidad nula - Gómez Zúñiga, Ricardo Emanuel (2025)
In this work, we solve Einstein’s field equations to find a compact star model who’s interior spacetime is given by the well-known Buchdahl-Vaidya-Tikekar metric with zero complexity for self-gravitating spheres. To this end, we conduct a bibliographic survey of interior solutions in general relativity and develop the field equations for a self-gravitating sphere with the proposed metric. Based on the stability and physical acceptability analysis, it is demonstrated that the obtained model meets the necessary conditions to represent a realistic compact star. The zero-complexity approach allows simplifying the structure of the system, thanks to the ability to compensate for inhomogeneities in the energy density and its anisotropy without compromising the physical validity of the solution, ensuring a coherent relationship between energy density, pressures, and anisotropy. The results indicate that the model star is stable and physically variable within general relativity since it meets all the conditions for physical acceptability. Finally, possible extensions of the model are suggested, including the incorporation of electric charge, extra dimensions, and dynamic perturbation studies to evaluate its behavior in more general scenarios. Comparisons of observational data are also proposed, varying parameters to validate the veracity of the research.