Absorption and scattering of massless scalar waves by black holes in quasi-topological gravity

TL;DR

The paper studies massless scalar perturbations around a family of regular black holes in quasi-topological gravity across $D\ge4$ dimensions, employing a partial-wave framework to compute absorption and scattering cross sections and a WKB approach for quasinormal modes. It demonstrates that higher spacetime dimension $D$ raises both the real and imaginary parts of the QNMs, while increasing the higher-curvature coupling $\alpha$ reduces absorption but enhances scattering, with pronounced effects at low frequencies. The results reveal distinct dimensional and coupling dependencies in the near-horizon potential and oscillatory cross-section behavior, including a low-frequency absorption enhancement for certain parameter ranges. These findings offer potential tools for distinguishing black hole solutions via scattering/absorption spectra and suggest connections to broader gauge-theory methods and topological black hole constructions.

Abstract

We consider massless scalar field perturbations of regular black holes in quasi-topological gravity. After reviewing various regular black hole solutions, we compute the total absorption cross-section and the partial absorption cross-section for different choices of the parameters using the partial wave method. The results show that the larger the parameter $α$, introduced in the context of quasi-topological gravity, the smaller the total absorption cross-section. In addition, we find that the influence of the space-time dimension ${D}$ on the absorption and scattering of massless scalar waves in this set of regular black holes differs from earlier computations.

Figures (6)

• Figure 1: The figure presents the effective potential profiles: Panel (A) corresponds to Eq. (\ref{['eq2']}) with parameter configurations . Panels (B)-(F) display effective potentials derived from the five distinct metrics discussed earlier.
• Figure 2: The figure illustrates the effective potential differences across varying spacetime dimensions $D$ and angular momentum quantum numbers $l$, with respect to Eq. (\ref{['eq2']}) as the reference baseline.
• Figure 3: The figure above presents the numerical results for the real part $\text{Re}(\omega)$ and imaginary part $\text{Im}(\omega)$ of the QNMs corresponding to the five aforementioned metrics.
• Figure 4: Left Figure illustrates the total absorption cross-section $\sigma_{\text{abs}}$ corresponding to the metric (\ref{['eq4']}) for different spacetime dimensions. Right Figure shows the total absorption cross-section $\sigma_{\text{abs}}$ corresponding to the metric (\ref{['eq4']}).
• Figure 5: Analysis of Partial and Total Absorption Cross-Sections for Different Black Hole Solutions.