Gravitational signatures of a non--commutative stable black hole

Abstract

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 \textit{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 $\Theta$ significantly impacts the paths of light and event horizons. Also, we calculate the shadows, which show that larger values of $\Theta$ correspond to larger shadow radii, and provide some constraints on $\Theta$ applying the observation of Sgr $A^{\ast }$ from the Event Horizon Telescope. Finally, we explore the deflection angle in this context.

38 pages, 11 figures and 6 tables

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