Exploring Non--commutativity as a Perturbation in the Schwarzschild Black Hole: Quasinormal Modes, Scattering, and Shadows

TL;DR

This paper investigates how introducing non-commutativity as a perturbation affects the scattering, quasinormal modes, shadows, and light trajectories of a Schwarzschild black hole, providing new insights into non-commutative spacetime effects.

Contribution

It presents a novel approach to incorporating non-commutativity into black hole scattering analysis, including reformulating the Klein-Gordon equation and analyzing various physical phenomena.

Findings

Non-commutativity alters quasinormal mode frequencies.

Shadow radius and light trajectories are affected by non-commutative parameters.

Greybody factors and absorption cross sections show significant deviations.

Abstract

In this work, by a novel approach to studying the scattering of a Schwarzschild black hole, the non-commutativity is introduced as a perturbation. We begin by reformulating the Klein-Gordon equation for the scalar field in a new form that takes into account the deformed non-commutative spacetime. Using this formulation, an effective potential for the scattering process is derived. To calculate the quasinormal modes, we employ the WKB method and also utilize fitting techniques to investigate the impact of non-commutativity on the scalar quasinormal modes. We thoroughly analyze the results obtained from these different methods. Moreover, the greybody factor and absorption cross section are investigated. Additionally, we explore the behavior of null geodesics in the presence of non-commutativity. Specifically, we examine the photonic, and shadow radius as well as the light trajectories for different non-commutative parameters. Therefore, by addressing these various aspects, we aim to provide a comprehensive understanding of the influence of non-commutativity on the scattering of a Schwarzschild-like black hole and its implications for the behavior of scalar fields and light trajectories.