4.5 Article

Geodesic stability and quasinormal modes of non-commutative Schwarzschild black hole employing Lyapunov exponent

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EUROPEAN PHYSICAL JOURNAL PLUS
卷 137, 期 2, 页码 -

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SPRINGER HEIDELBERG
DOI: 10.1140/epjp/s13360-022-02403-5

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  1. University Grants Commission (UGC), New Delhi, India [1479/CSIR-UGC NET-JUNE-2017]
  2. Science and Engineering Research Board (SERB), India [EMR/2017/000339]

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This paper investigates the dynamics of test particles and the stability of circular geodesics in a non-commutative geometry-inspired Schwarzschild black hole spacetime. The study analyzes the Lyapunov exponent and stability of equatorial circular geodesics for both massive and massless test particles, considering different values of the non-commutative parameter (alpha). The instability of null circular orbits is also discussed, and the quasinormal modes for massless scalar field perturbation are evaluated and visualized by relating the angular frequency and Lyapunov exponent.
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 (lambda(c)) 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 (alpha). 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 (alpha) and angular momentum of perturbation (l), is also observed and discussed.

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