Chaotic imprints of dark matter in extreme mass-ratio inspirals

Abstract

Extreme mass-ratio inspirals (EMRIs) are among the most powerful probes of strong-field gravity and of the environments surrounding supermassive compact objects. Motivated by the expected presence of dark matter near galactic centers, we investigate the emergence and gravitational-wave imprints of chaotic dynamics in EMRIs evolving in non-vacuum spacetimes. Within a unified dynamical framework, we analyze test-particle motion in a broad class of dark-matter-embedded geometries, including singular black holes, regular black holes, naked singularities, and Einstein-cluster configurations. We show that environmental perturbations generically break integrability in the strong-field regime, giving rise to chaotic motion whose onset, duration, and termination depend sensitively on horizon structure, core regularization, and matter distribution. Using the numerical Kludge approach, we demonstrate that chaotic trajectories produce systematic qualitative modifications of the emitted gravitational radiation, such as irregular amplitude modulation and loss of phase coherence, in contrast to the smooth, quasi-periodic waveforms generated by regular motion. Our results establish the robustness of chaos in environmentally perturbed EMRIs and provide a clear conceptual link between nonlinear orbital dynamics, spacetime structure, and observable gravitational-wave signatures.

Figures (11)

• Figure 1: Orbital projections onto the equatorial plane ($\theta=\pi/2$) in the spacetime described by metric \ref{['metric1']}, for $E=100$ and $r_s=0.5$. The integration interval is $0 \le t \le 6000$ (in units of $M$). Upper panel: Non-chaotic motion for $\rho_s=0.09$, corresponding to horizon radius $r_h=2.16$. Lower panel: Chaotic motion for $\rho_s=0.2$, corresponding to $r_h=2.36$. Units $G=c=M=1$ are adopted.
• Figure 2: Orbital projections onto the equatorial plane ($\theta=\pi/2$) in the Bronnikov-type geometry \ref{['eq:bronnikov_metric']}, for $E=227$, $\rho_s=0.07$, and $r_s=0.5$. The corresponding horizon radius is $r_h=1.94$. Upper panel: Chaotic trajectory integrated over $0 \le t \le 5000$ (in units of $M$), terminating at $(x,\,y)=(4.26,\, 2.65)$ prior to plunge. Lower panel: Chaotic trajectory integrated over $0 \le t \le 5800$, ultimately ending at the central singularity $(x,y)=(0,0)$. Units $G=c=M=1$ are used.
• Figure 3: Orbital projection onto the equatorial plane ($\theta=\pi/2$) in the Bronnikov-type spacetime \ref{['eq:bronnikov_metric']}, for $E=230$, $\rho_s=0.07$, and $r_s=0.5$. The corresponding horizon radius is $r_h=1.94$. The trajectory is integrated over the interval $0 \le t \le 2000$ (in units of $M$). Units $G=c=M=1$ are adopted.
• Figure 4: Poincaré sections constructed at $\phi=0.5$ for the Simpson-Visser spacetime \ref{['eq:sv_metric']}. Initial conditions are $(r(0),\phi(0),p_r(0))=(3.0,0.1,0.1)$ (black points) and $(3.0,-0.1,-0.1)$ (blue points). The integration interval is $0 \le t \le 5\times10^{4}$ (in units of $M$). Upper panel: Dependence on the regularization parameter $a$ for fixed $E=100$ and $a=0.05,0.5,1.5$. Lower panel: Dependence on the orbital energy $E$ for fixed $a=0.05$ and $E=100,140,180$. Units $G=c=M=1$ are adopted.
• Figure 5: Orbital projections onto the equatorial plane ($\theta=\pi/2$) in the spacetime \ref{['ns']}, corresponding to the case where the central mass $M$ exceeds the dark-matter mass contribution ($M > M_{\rm DM}$). In this regime, the naked singularity is located at $r=r_+$. The trajectories are shown for $E=50$ and $r_- = 0.1,0.5,1.5$. Units $G=c=M=1$ are adopted.