Non-Linear Force Dynamics in Black Hole Accretion Disks Using Logarithmic and Trigonometric Approximations

Authors

Adi Suarman Situmorang , Juli Antasari Br Sinaga , Ratna Rintaningrum , Ruben Cornelius Siagian

DOI:

10.29303/jppipa.v11i2.10291

Published:

2025-02-28

Issue:

Vol. 11 No. 2 (2025): February

Keywords:

Accretion disks, Force calculations, Non-linear dynamics, Rotating black holes, Spin parameters

Research Articles

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Situmorang, A. S., Sinaga, J. A. B., Rintaningrum, R., & Siagian, R. C. (2025). Non-Linear Force Dynamics in Black Hole Accretion Disks Using Logarithmic and Trigonometric Approximations . Jurnal Penelitian Pendidikan IPA, 11(2), 988–1000. https://doi.org/10.29303/jppipa.v11i2.10291

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Abstract

Accretion disks are material structures that form when gas, dust or plasma is pulled towards a black hole by its strong gravity. In rotating (Kerr) black holes, the dynamics of the accretion disk becomes more complex due to frame-dragging effects that affect particle trajectories and energy release patterns. This study aims to develop an algorithm for calculating the force F(x) on particles in the accretion disk by considering the non-linear interaction between the black hole spin parameter and the relative position of the particles. The developed algorithm uses logarithmic and trigonometric approaches to improve the accuracy of the force calculation. The results show that variations in the spin parameter and relative position significantly affect the force distribution in the accretion disk. Visualization of the force interaction reveals the existence of non-linear patterns that contribute to the system dynamics. The main contribution of this research is the refinement of force calculation models that previously did not fully incorporate the combined effects of logarithmic and trigonometry in particle interactions. The proposed approach offers a more accurate predictive tool to explore the physical processes around black holes, and supports the interpretation of observational data from telescopes and gravitational wave detectors

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Author Biographies

Adi Suarman Situmorang, HKBP Nommensen University

Juli Antasari Br Sinaga, HKBP Nommensen University

Ratna Rintaningrum, Institute of Technology Sepuluh Nopember

Ruben Cornelius Siagian

Ruben Cornelius Siagian, born in Medan, Sumatra, Indonesia, is a scientific scholar with a Bachelor of Science (B.Sc) degree and a specialized focus in computational and theoretical physics, astronomy, and cosmology. With experience as a high school and junior high school teacher at a tutoring center, providing instruction in science, particularly physics and mathematics, Ruben has also conducted several published research studies indexed nationally and internationally. He has authored numerous books and scientific articles related to theoretical and computational physics.

Ruben's membership in the Indonesian Physics Organization showcases his commitment to providing insights to students about the importance of a thirst for knowledge in the natural sciences. However, his interests extend beyond the realm of science alone. Ruben strives to balance his passion for science with his love for nationalism, aiming to provide understanding to students about national unity and the importance of respecting religious, ethnic, and cultural diversity.

In terms of organizational involvement, Ruben has served as the Deputy Secretary of Education Cadre in the GMKI Organization's FMIPA Branch and as the Vice Chairman of the FMIPA Student Senate at Universitas Negeri Medan. With several achievements in science olympiads, Ruben possesses a strong motivation to contribute to the advancement of education in Indonesia, which is still partly constrained by a monotonous curriculum.

Ruben Siagian is an inspirational scholar dedicated to the progress of science and education in Indonesia. His passion, dedication, and commitment make him a valuable asset to the scientific and educational landscape of the country.

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Copyright (c) 2025 Adi Suarman Situmorang, Juli Antasari Br Sinaga, Ratna Rintaningrum, Ruben Cornelius Siagian

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