Scattering sections from regular black holes immersed in perfect fluid dark matter

TL;DR

The paper analyzes how perfect fluid dark matter (PFDM) surrounding regular black holes alters scattering cross sections, using classical geodesic, semi-classical glory, and full partial-wave methods for Hayward, Bardeen, and Ayón-Beato-García BHs. PFDM enters the spacetime via $f(r)=1-rac{2m(r)}{r}$ with a PFDM term $\frac{\alpha}{2}\ln\left(\frac{r}{|\alpha|}\right)$ in $m(r)$, influencing both the deflection angle $\theta(b)$ and wave interference patterns. The results show PFDM generally increases the scattering cross section and narrows the interference fringes in the semi-classical regime, with ABG often yielding the strongest effects; partial-wave calculations corroborate these trends and align with glory at large angles and with classical theory at small angles. Together, the findings provide a consistent, multi-method view of how dark-matter environments modify BH scattering and extend prior PFDMBH work (e.g., Tovar:2025apz).

Abstract

In this contribution, we investigate the scattering cross sections of black holes immersed in perfect fluid dark matter (PFDM). We present both the classical and semi-classical scattering cross sections for different values of the parameter that characterizes the PFDM contribution. Our results show that the presence of dark matter increases the classical scattering cross section and modifies the width of the interference fringes in the semi-classical regime. In addition, the scattering cross section is also computed using the partial wave method for the black holes considered, exhibiting similar qualitative behavior. These findings suggest that the effects of dark matter surrounding black holes may play an important role in black holes phenomenology, particularly in certain regions near the black hole.

Figures (5)

• Figure 1: Density plots of the parameter ranges for which the Hayward black hole (a), the Bardeen black hole (b), and the Ayón–Beato–García black hole (c) immersed in PFDM exhibit two event horizons. The darker regions indicate the combinations of parameters for which the BHs admits two horizons. Panel (d) shows a comparison of the corresponding regions for the three BH models.
• Figure 2: Classical scattering cross sections for black holes immersed in PFDM: (a) Hayward black hole, (b) Bardeen black hole and (c) Ayón–Beato–García black hole are shown for different values of the parameter $\alpha/M$. Panel (d) presents a comparative analysis of the scattering cross sections for the BHs with $\alpha/ M = -0.4$. For the different panels, we consider $(\epsilon/M)^{2}=(g/M)^{2}=(q/M)^{2}=0.6$
• Figure 3: Semi-classical scattering cross sections for black holes immersed in PFDM: (a) Hayward black hole, (b) Bardeen black hole, and (c) Ayón–Beato–García black hole are shown for different values of $\alpha / M$. Panel (d) presents a comparative analysis of the semi-classical scattering cross sections for the BHs with $\alpha / M = -0.4$. For the different panels, we consider $(\epsilon/M)^{2}=(g/M)^{2}=(q/M)^{2}=0.6$ and $M\omega=2$
• Figure 4: Scattering cross sections for black holes immersed in PFDM: (a) Hayward black hole, (b) Bardeen black hole and (c) Ayón–Beato–García black hole are shown for different values of $\alpha /M$. Panel (d) presents a comparative analysis of the scattering cross sections for the BHs with $\alpha / M = -0.4$. For the different panels, we consider $(\epsilon/M)^{2}=(g/M)^{2}=(q/M)^{2}=0.6$ and $M\omega=2$
• Figure 5: Scattering cross sections for black holes immersed in PFDM: (a) Hayward black hole, (b) Bardeen black hole and (c) Ayón–Beato–García black hole, shown for $\alpha/M=-0.3$, $M\omega=2$ and $(\epsilon/M)^{2}=(g/M)^{2}=(q/M)^{2}=0.6$.