Scattering and absorption sections by an improved Schwarzschild black hole

Abstract

In this contribution, we investigate the scattering and absorption sections of the improved Schwarzschild black hole. The differential scattering section is analysed using three complementary approaches: the classical approximation, the semi-classical approximation, and the partial wave technique. We show that, while the classical scattering section exhibits only small deviations from the standard Schwarzschild case, the semi-classical and partial wave analyses reveal differences in the interference pattern and in the amplitude. Also, the absorption section is computed using the partial wave method and compared with the sinc approximation. We find that both approaches present deviations that appear in the low-frequency regime, where the partial wave result approaches the horizon area. Our results indicate that quantum corrections in the Schwarzschild can lead to modifications in scattering and absorption properties, providing further insight into the phenomenology of quantum corrected black holes.

Figures (6)

• Figure 1: a) The blue line in the plot on the left represents the evolution of the mass as a function of the radius $r$; the red dotted and black dotted lines are the critical mass $M_c = 3.50274$ and $M = 4.1$ respectively. The critical value $r_c=4.4841$ and the horizon radii $r_{in}=3.3584$ and $r_{out}=6.8497$ are also shown. b) The plot shows the evolution of $f(r)$ where we can see that the number of event horizons depends on the mass value.
• Figure 2: a) Comparison of the classical scattering cross section for the improved Schwarzschild BH and the Schwarzschild BH with $M=4$. b) Behaviour of the normalized critical impact parameter $b_{c} M^{-1}$ for the improved Schwarzschild BH
• Figure 3: The graphs show the behavior of semi-classical scattering section for improved Schwarzschild and Schwarzschild BHs with $M=4$. In the figure a), we use $M\omega=2$, while in figure b) we use $M\omega=1.5$.
• Figure 4: Behavior of scalar differential scattering section of improved Schwarzschild BH with $M=4$ and Schwarzschild BHs. In the figure a), we use $M\omega=2$, while in the figure b) $M\omega=1.5$.
• Figure 5: Comparison of partial wave, semi-classical and classical approaches for the scattering section, for $M = 4$ with $M\omega = 2$ (figure a)) and $M\omega = 1.5$ ( figure b)) for the improved Schwarzschild BH.