Shadow of a Noncommutative Thin-Shell Gravastar

One of the main challenges in astronomy is the direct observation of black holes. However, differentiating them from black holes through photon observations can be difficult if Ultra-Compact Objects with unstable circular photon orbits exist. An example of an Ultra-Compact Object is a Gravastar (gravitational vacuum star), initially proposed by Mazur and Mottola. For definition purposes, we construct a spherically symmetric thin-shell gravastar model within a noncommutative model, in which these effects are integrated by a Lorentzian distribution of the energy density with minimum width $\sqrt{\theta}$. The model is constructed using the cut-and-paste technique to connect a nonsingular de Sitter interior to a noncommutative Schwarzschild exterior, satisfying the Israel junction conditions on the interface hypersurface $\Sigma$. We examine the stability of the model through its energy conditions, highlighting the influence of the noncommutative parameter on its behavior. The stability analysis of our current model is also studied by introducing the parameter $\eta$, and we explore the stability region where the gravastar becomes stable. We then also show that, due to noncommutativity, the proximity and deflection of photons change when we increase the noncommutative parameter. Our proposed gravastar model, with noncommutative geometry on its exterior, can be considered a stable and viable alternative to the charged black hole in the context of this gravity.