Chaotic motion of particle in regular black hole supported by Galactic halo

Abstract

We investigate the chaotic dynamics of the massless test particles moving in the regular black hole supported by a Dehnen-type dark matter halo. By limiting the particle within a external harmonic potential, we employ Poincaré sections and Lyapunov exponents as diagnostic tools and analyze the transition from regular to chaotic motion as the halo scale parameter $a$ increase. These findings indicate that the galactic halo acts as a primary driver of chaos in this regular black hole geometry, significantly distorting the phase space structure near the potential center, acting as a primary driver of chaos. Crucially, our results elucidate the distinct imprint of dark matter halos on particle dynamics, suggesting that observing such chaotic signatures in astrophysical systems could provide a novel method for detecting and constraining the properties of dark matter in future observations.

Figures (3)

• Figure 1: The inner($r_-$) and outer($r_+$) horizon of the regular black hole for $a\in (0,1]$
• Figure 2: Poincaré sections recording particle crossings at $\theta=\pi/2$ with $p_\theta>0$. The energy is fixed to be $E=50$. The six panels correspond to different values of the halo scale parameter $a$, specifically $a=0, \frac{1}{8}, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1$. Initial conditions are randomly sampled within $r_{int} \in [3, 3.4]$, $p_r{}_{int} \in [-1, 1]$, and $\theta_{int} \in [13\pi/30, 17\pi/30]$, with distinct colors representing different initial condition. The harmonic potential center is located at $r_0=3.2$ and $\theta_0=\pi/2$ and the spring constant is $K_r=100$ and $K_\theta=25$.
• Figure 3: The Lyapunov exponent as a function of time for different values of the halo scale parameter $a$, specifically $a=0$(Blue), $a=1/2$(Red) and $a=1$(Orange).