Gravitational signatures of a non--commutative stable black hole

TL;DR

This paper explores the effects of non-commutative geometry on black hole properties, including thermodynamics, quasinormal modes, geodesics, shadows, and light deflection, revealing how non-commutative parameters influence observable phenomena.

Contribution

It provides a comprehensive analysis of non-commutative black holes, combining thermodynamics, wave dynamics, and observational signatures, with new constraints on non-commutative parameters from astrophysical data.

Findings

Stronger non-commutative parameters slow damping of gravitational waves

Larger non-commutative parameters increase shadow size

Non-commutative parameters significantly affect particle trajectories

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 P\"oschl--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 $A^{*}$ from the Event Horizon Telescope. Finally, we explore the deflection angle in this context.