Anisotropic Thin Shell Around a 3 Solar Masses Core:

​We present a model investigating whether collapsing matter of a mass around three solar masses can avoid a singularity by forming a rigid thin shell with anisotropic stresses surrounding a regular fluid core. The interior core is described by an anisotropic structural system with a specific pressure closure and pressure anisotropy, while the boundary is governed by standard geometric junction conditions. Static configurations adhering to the dominant energy condition exist within a defined external compactness window for specified core parameters and central densities, with stable configurations further restricted by a causal shell stiffness limit. Through a linear radial stability analysis that explicitly incorporates matter flux across the shell, we determine the critical shell stiffness required for stability. We show analytically that the sign of energy flux originates strictly from the boundary normal orientation. Furthermore, for a vacuum interior, we derive a closed-form analytic expression for the critical stiffness, which reproduces the numerical core results closely, demonstrating that stability is primarily governed by exterior geometry. Finally, estimating the shell thickness indicates that at standard nuclear density, the thickness-to-radius ratio violates the thin-shell approximation, requiring extreme densities within the shell for self-consistency.