Epicyclic motion of charged particles around a weakly magnetized Kiselev black hole

TL;DR

This work analyzes charged-particle dynamics around a weakly magnetized Kiselev black hole by formulating an effective potential that incorporates quintessence and Lorentz forces. It characterizes bound motion, stable circular orbits, ISCO conditions, and epicyclic frequencies, revealing off-equatorial saddle points generated by quintessence and a maximal bound radius r_* determined by the quintessence parameters. The study shows how the combination of a magnetic field and quintessence modifies radial and latitudinal frequencies, periastron precession, and gravitational Larmor precession, producing qualitative differences from Ernst and pure Kiselev spacetimes. The results have potential observational relevance for accretion dynamics and for constraining quintessence and external magnetic fields near black holes.

Abstract

We investigate the motion of charged particles evolving around a magnetized Kiselev black hole, in the weak magnetic field approximation. The effective potential allows us to study the bound motion and the stable circular orbits. We analyze the impact of combined quintessence and magnetic fields on the epicyclic frequencies. Finally, we examine the periapsis shift and gravitational Larmor precession pointing out differences from the Ernst or Kiselev spacetimes.

Figures (21)

• Figure 1: Plot of the surface (cyan color) $f=0$ as a function of $r$, $w$ and $k$. The horizontal planes corresponds to fixed values of $k$. The fixed values of $k$ are represented by the horizontal planes, the red one corresponds to $k=0.01$, blue to $k=0.05$ and green one to $k=0.1$. Here we used $M=1$.
• Figure 2: Left panel. Plot of $E_{\min}^2$ (solid curves) and $E_{s 1}^2$ (dashed horizontal lines) as functions of $b>0$ for different values of $k$. Right panel. Plot of $E_{\min}^2$ (solid curves) and $E_{s2}^2$ (dashed curves) as functions of $b<0$, for different values of $k$. The black dots represent the critical values $b_{cr}$ for which $E_{\min}^2=E_{s 1, s2}^2$. The other values of the parameters are: $M=1$, $w=-2/3$ and $L=4$.
• Figure 3: Left panel. Plot of the effective potential (\ref{['V']}) and the bound particle trajectory in the $(x,z)-$ plane. The energy $E^2=0.58$ is represented by the light blue horizontal plane. The equipotential curve given by the solutions of the equation $E^2=V$ is represented by the red curves. The equatorial plane corresponding to $z=0$ is represented by the dashed black line. Right panel. 3D plot of the bound trajectory of a particle moving in the potential represented in the left panel. The gray sphere represents the horizon $r_-=2.09$. The values of the parameters are: $M=1$, $w=-2/3$, $k=0.02$, $b=0.10$ and $L=4$.
• Figure 4: Left panel. Plot of the effective potential (\ref{['V']}) and the particle trajectory in the $(x,z)-$ plane. The equipotential curve given by the solutions of the equation $E^2=V$ is represented by the red curve. The equatorial plane corresponding to $z=0$ is represented by the dashed black line. The energy $E^2=0.52$ is represented by the light blue plane. Right panel. 3D plot of the escape trajectory of a particle moving in the potential represented in the left panel. The gray sphere represents the horizon $r_-=2.14$. The values of the parameters are: $M=1$, $w=-2/3$, $k=0.03$, $b=0.10$ and $L=4$.
• Figure 5: The effective potential (\ref{['V0']}) as a function of $b$ and $r \in [r_- , r_+ ]$. The value of the quintessence parameter is $k=0.015$ in the left panel and $k=0.04$ in the right panel. The other numerical values are: $M=1$, $w=-2/3$ and $L=6$.