https://doi.org/10.1140/epjc/s10052-025-14280-0
Regular Article - Theoretical Physics
Testing of QPOs, particle dynamics, emission energy and thermal fluctuation around a regular hairy black hole
1
School of Mathematical Sciences, Zhejiang Normal University, 321004, Jinhua, Zhejiang, China
2
Research Center of Astrophysics and Cosmology, Khazar University, 41 Mehseti Street, AZ1096, Baku, Azerbaijan
3
Department of Mathematics, School of Science, University of Management and Technology, 54000, Lahore, Pakistan
4
Department of Mathematics and Statistics, The University of Lahore, 1-KM Defence Road, 54000, Lahore, Pakistan
5
Department of Mathematical and Physical Sciences, College of Arts and Sciences, University of Nizwa, 616, Nizwa, Sultanate of Oman
6
Centre for Cosmology, Astrophysics and Space Science (CCASS), GLA University, 281406, Mathura, Uttar Pradesh, India
7
School of Science, Walailak University, 80160, Nakhon Si Thammarat, Thailand
8
College of Graduate Studies, Walailak University, 80160, Nakhon Si Thammarat, Thailand
9
New Uzbekistan University, Movarounnahr street 1, 100000, Tashkent, Uzbekistan
10
Urgench State University, Kh. Alimdjan Str. 14, 220100, Urgench, Uzbekistan
a
phongpichit.ch@mail.wu.ac.th
Received:
16
December
2024
Accepted:
4
May
2025
Published online:
10
June
2025
We investigate the dynamics of test particles around a spherically symmetric, non-rotating, hairy regular black hole, examining how the model parameters affect particle motion. The black hole is characterized by two parameters, the mass 
and a hairy parameter 
. Using the effective potential, we examine the stability of circular orbits. We derive analytical expressions for the energy and angular momentum of test particles as a function of the black hole parameters. The effective forces acting on particles and the innermost stable circular orbits are also examined. Additionally, we numerically integrate the equations of motion to examine particle trajectories and further investigate their motion. Epicyclic oscillations of test particles close to the equatorial plane are explored, and analytical expressions for radial, vertical, and orbital frequencies are derived as functions of the black hole parameters. We also examine the frequency of periastron precession of the particles. We compare the motion of test particles around a hairy regular black hole with the particle motion around a classical non-rotating Schwarzschild black hole. Further, we discuss thermally fluctuating phenomena by using the Tsallis entropy and the energy emission process. Our findings show that the black hole model’s parameters significantly impact particle motion and thermal features.
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
