In this paper, we explore the evolution of a Dirac oscillator (DO) field within the near-horizon region of the Banados, Teitelboim, and Zanelli (BTZ) black hole (BH) by seeking exact solutions to the corresponding DO equation. We obtain the relativistic frequency expression and analyze the impact of various parameters implicated in it. Our findings reveal that the damped mode of this fermionic oscillator field relies on the BH mass, spin of the fermionic field, and frequency of the oscillator field. Lastly, we focus on the quantum system for a zero oscillator frequency as a specific case and thoroughly analyze the obtained results.
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Güvendi et al. (2024) studied this question.
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