Researchers have developed a theoretical model of ultracompact objects, such as neutron stars or gravastars, that incorporates anisotropic pressure. This new approach allows for the existence of stellar configurations with extreme compactness, surpassing the Buchdahl limit and approaching arbitrarily close to the Schwarzschild radius of a black hole. The model assumes homogeneous density and uses a covariant anisotropic equation of state, providing a richer description of the internal structure of these exotic objects within the framework of General Relativity.

The study reveals two distinct regimes in the parameter space of compactness and anisotropy, separated by a critical curve. The first regime corresponds to regular anisotropic configurations with positive central pressure. However, the second regime presents singular configurations with negative central pressure, regardless of the degree of anisotropy. To address this pressure divergence, the authors propose introducing a thick shell into the model, which eliminates the singularity and yields regular ultracompact gravastar configurations. This "thick-shell" method is applied to both anisotropic and isotropic gravastar models.

This work is relevant because it explores alternatives to black holes as end-states of stellar evolution, offering a detailed description of how anisotropy in internal pressure could influence the structure and stability of extremely dense objects. The ability to construct models that exceed the Buchdahl limit and approach the event horizon without forming one provides new avenues for understanding the physics of matter under extreme gravitational and density conditions, and could have implications for the interpretation of astrophysical observations of compact objects.