https://doi.org/10.1140/epjp/s13360-022-02403-5
Regular Article
Geodesic stability and quasinormal modes of non-commutative Schwarzschild black hole employing Lyapunov exponent
1
Department of Physics, Gurukula Kangri (Deemed to be University), 249 404, Haridwar, Uttarakhand, India
2
Center for Space Research, North-West University, 2745, Mahikeng, South Africa
3
Department of Applied Science, Faculty of Engineering and Technology, Gurukula Kangri (Deemed to be University), 249 404, Haridwar, India
4
Astrophysics Research Centre, School of Mathematics, Statastics and Computer Science, University of KwaZulu-Natal, X54001, 4000, Durban, South Africa
Received:
26
October
2021
Accepted:
18
January
2022
Published online:
28
January
2022
We study the dynamics of test particle and stability of circular geodesics in the gravitational field of a non-commutative geometry-inspired Schwarzschild black hole spacetime. The coordinate time Lyapunov exponent (
) is crucial to investigate the stability of equatorial circular geodesics of massive and massless test particles. The stability or instability of circular orbits is discussed by analyzing the variation of Lyapunov exponent with radius of these orbits for different values of non-commutative parameter (
). In the case of null circular orbits, the instability exponent is calculated and presented to discuss the instability of null circular orbits. Further, by relating parameters corresponding to null circular geodesics (i.e., angular frequency and Lyapunov exponent), the quasinormal modes for a massless scalar field perturbation in the eikonal approximation are evaluated and also visualized by relating the real and imaginary parts. The nature of scalar field potential, by varying the non-commutative parameter () and angular momentum of perturbation (l), is also observed and discussed.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
