Gravitational signatures of a non-commutative stable black hole

This work investigates several key aspects of a non-commutative theory with mass deformation. We calculate thermodynamic properties of the system and compare our results with recent literature. We examine the quasinormal modes of massless scalar perturbations using two approaches: the WKB approximation and the Pöschl–Teller fitting method. Our results indicate that stronger non-commutative parameters lead to slower damping oscillations of gravitational waves and higher partial absorption cross sections. Furthermore, we study the geodesics of massless and massive particles, highlighting that the non-commutative parameter Θ significantly impacts the paths of light and event horizons. Also, we calculate the shadows, which show that larger values of Θ correspond to larger shadow radii, and provide some constraints on Θ applying the observation of Sgr A∗ from the Event Horizon Telescope. Finally, we explore the deflection angle in this context.