https://doi.org/10.1140/epjc/s10052-024-12889-1
Regular Article - Theoretical Physics
Exploring non-commutativity as a perturbation in the Schwarzschild black hole: quasinormal modes, scattering, and shadows
1
Faculty of Physics, Shahrood University of Technology, Shahrood, Iran
2
Department of Physics, University of Hradec Králové, Rokitanského 62, 500 03, Hradec Králové, Czechia
3
Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Universidad de Valencia, 46100, Burjassot, Valencia, Spain
Received:
21
October
2023
Accepted:
7
May
2024
Published online:
4
June
2024
In this work, by a novel approach to studying the scattering of a Schwarzschild black hole, the non-commutativity is introduced as 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.
© The Author(s) 2024
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