Plasma lensing, epicyclic oscillations, particle collision, and thermal fluctuations around a short-hairy black hole

Abstract

We explore the behavior of test particles in the vicinity of a spherically symmetric black hole with short-hair characteristics, emphasizing the impact of the model’s parameters on various phenomena such as particle trajectories, plasma-induced gravitational lensing, epicyclic oscillations, and thermal variations. The black hole is defined by three key parameters: mass $M$, the short-hairy parameter $Q$, and an additional parameter $\alpha$. We derive analytical formulas for the energy and angular momentum of test particles, expressed in terms of these black hole parameters. Additionally, we investigate the effective potential, the innermost stable circular orbits, and the forces influencing particle motion. The study also delves into the epicyclic oscillations of particles close to the equatorial plane, providing analytical expressions for radial, vertical, and orbital frequencies, along with the periastron precession frequency. In the context of weak gravitational lensing with plasma, we observe that the parameter $\alpha$ does not affect the deflection angle, whereas the other parameters play a significant role. Moreover, we analyze thermal fluctuations in these short-hairy black holes, which are linked to the Hawking temperature and entropy. Our findings underscore the profound influence of the black hole’s parameters on particle dynamics, revealing fascinating aspects of their behavior.