Impact of Multipole Parameters on Black Hole Gravitational Fields: A Regge-Wheeler Potential Analysis - Ruben Cornelius Siagian; Kevin William Andri Siahaan; Taufik Roni Sahroni; Rohana Hassan (Jurnal Fisika Flux: Jurnal Ilmiah Fisika FMIPA Universitas Lambung Mangkurat, 2025)
This study analyzes the effect of multipole values (\( \ell\)) on the distribution of gravitational or electromagnetic fields in black holes, using the Regge-Wheeler potential approach. Various masses (5, 10, 20, 50) and varying \( \ell\) values are analyzed to explore the impact of multipole on space-time geometry. The results show that increasing the value of \( \ell\) reduces the values of \( r_{\text{positive}}\) and \( r_{\text{negative}}\), which indicates the field distribution becomes more focused at higher multipole values. The sensitivity to changes in the \( \ell\) value is especially noticeable in the colinear \( \ell\) interval between 5 to 17, where small changes in the \( \ell\) value result in large changes in the \( r\) value. In the framework of black hole theory, two solutions of the quadratic equation \( \ell = \frac{-1 ±\sqrt{13}}{2}\) yield two values \( \ell_+\) and \( \ell_-\), which affect the distribution of the gravitational field. Logarithmic analysis of the \( r \) value reveals variations in the field distribution in the multipole range, and shows a strong dependence on the black hole mass, with more significant changes at small masses. This study provides a deeper understanding of the dependence of the field distribution on multipole and opens up opportunities for further research into the complexity of multipolar interactions in black hole theory.