Chaotic motion and power spectral density in Schwarzschild Bertotti-Robinson black hole spacetime

Abstract

In this paper, we show that in weak field limit Schwarzschild Bertotti-Robinson black hole (Schwarzschild-BR BH) turns into Schwarzschild black hole immersed in external uniform magnetic field which is given in 1. The dynamics of both magnetized and electrically charged particles in the vicinity of a Schwarzschild-BR black hole are investigated. The innermost stable circular orbits (ISCOs) for both magnetized and electrically charged particles are examined in detail, revealing that the magnetic field parameter B exerts a considerable influence, leading to an increase in the ISCO radius. The orbital and epicyclic motion of test particles in Schwarzschild-BR black hole spacetime was analyzed, including both circular orbits and their oscillatory perturbations. Additionally, the trajectories of both magnetized and electrically charged particles are analyzed for various configurations of the magnetic parameter B. We also demonstrate how the magnetic field B, electric charge q, and magnetic moment μ influence the dynamics of charged particles, specifically affecting the chaotic behavior, Poincare' sections, oscillatory frequencies and power spectral density.

Figures (13)

• Figure 1: The variation of event horizon radius with magnetic field strength B in equatorial orbit.
• Figure 2: The plot shows the magnetic field lines in the vicinity of the Schwarzschild BR.
• Figure 3: The radial profile of the effective potential is depicted for fixed values of the magnetic moment $\mu$ (left panel), and the magnetic field $B$ (right panel). The minima ($r_{\text{min}}$) in the effective potential correspond to stable circular orbits, while the maxima ($r_{\text{max}}$) correspond to unstable circular orbits.
• Figure 4: Dependence of the ISCO radius $r_{\text{ISCO}}$, ISCO specific angular momentum $l_{\text{ISCO}}$, and the ISCO specific energy $E_{\text{ISCO}}$ on the magnetic field $B$.
• Figure 5: Specific energy $\mathcal{E}$ and angular momentum $l$ for circular orbits at fixed value of the magnetic dipole momentum $\mu$. Here, stable circular orbits are depicted by solid lines, and unstable circular orbits are represented by dashed lines.