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Scattering and Absorption of Standard Model Fields by Brane-Localized Schwarzschild--de Sitter Black Holes

Alexey Dubinsky

TL;DR

This work studies scalar, electromagnetic, and Dirac perturbations on a 3+1-dimensional brane embedded in a higher-dimensional Schwarzschild–de Sitter spacetime by projecting the Tangherlini bulk onto the brane. It computes grey-body factors and absorption cross-sections using a sixth-order WKB method and via a quasinormal-mode–transmission correspondence, exploring how the cosmological constant $\Lambda$ and field mass $\mu$ shape transmission and absorption. The results show that larger $\Lambda$ lowers the effective potential barrier, enhancing transmission at low to intermediate frequencies, while larger $\mu$ raises the threshold energy and suppresses low-frequency absorption; the GBF–QNM correspondence is reliable for $\ell\ge 2$ with deviations below ~1%. These findings illuminate how dimensionality and cosmological expansion influence brane-localized black-hole scattering and Hawking-like emission, with potential implications for holographic transport in higher-dimensional settings.

Abstract

We investigate the propagation and absorption of Standard Model fields -- scalar, electromagnetic, and Dirac -- on a 3+1-dimensional brane embedded in a higher-dimensional Schwarzschild--de Sitter (SdS) spacetime. Using the effective four-dimensional projection of the Tangherlini metric, we compute grey-body factors (GBFs) and absorption cross-sections for each spin sector by means of the sixth-order WKB method and, independently, via the recently proposed correspondence between quasinormal modes (QNMs) and transmission coefficients. The results demonstrate that the cosmological constant and field mass crucially affect the transmission probabilities: increasing $Λ$ lowers the potential barrier and enhances the transparency of the geometry, while a larger field mass $μ$ suppresses low-frequency emission and shifts the absorption spectrum to higher energies. For all fields, the QNM--GBF correspondence proves reliable to within about one percent for multipoles $\ell \ge 2$, while the correspondence remains less accurate for the lowest multipoles. The total absorption cross-sections exhibit the expected transition from the low-frequency suppression to the geometric-optics regime. Overall, these findings provide quantitative insight into the interplay between dimensionality, cosmological expansion, and black-hole radiation on the brane.

Scattering and Absorption of Standard Model Fields by Brane-Localized Schwarzschild--de Sitter Black Holes

TL;DR

This work studies scalar, electromagnetic, and Dirac perturbations on a 3+1-dimensional brane embedded in a higher-dimensional Schwarzschild–de Sitter spacetime by projecting the Tangherlini bulk onto the brane. It computes grey-body factors and absorption cross-sections using a sixth-order WKB method and via a quasinormal-mode–transmission correspondence, exploring how the cosmological constant and field mass shape transmission and absorption. The results show that larger lowers the effective potential barrier, enhancing transmission at low to intermediate frequencies, while larger raises the threshold energy and suppresses low-frequency absorption; the GBF–QNM correspondence is reliable for with deviations below ~1%. These findings illuminate how dimensionality and cosmological expansion influence brane-localized black-hole scattering and Hawking-like emission, with potential implications for holographic transport in higher-dimensional settings.

Abstract

We investigate the propagation and absorption of Standard Model fields -- scalar, electromagnetic, and Dirac -- on a 3+1-dimensional brane embedded in a higher-dimensional Schwarzschild--de Sitter (SdS) spacetime. Using the effective four-dimensional projection of the Tangherlini metric, we compute grey-body factors (GBFs) and absorption cross-sections for each spin sector by means of the sixth-order WKB method and, independently, via the recently proposed correspondence between quasinormal modes (QNMs) and transmission coefficients. The results demonstrate that the cosmological constant and field mass crucially affect the transmission probabilities: increasing lowers the potential barrier and enhances the transparency of the geometry, while a larger field mass suppresses low-frequency emission and shifts the absorption spectrum to higher energies. For all fields, the QNM--GBF correspondence proves reliable to within about one percent for multipoles , while the correspondence remains less accurate for the lowest multipoles. The total absorption cross-sections exhibit the expected transition from the low-frequency suppression to the geometric-optics regime. Overall, these findings provide quantitative insight into the interplay between dimensionality, cosmological expansion, and black-hole radiation on the brane.

Paper Structure

This paper contains 6 sections, 22 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Black-hole metric projected on the brane and wave-like equations.
  3. Grey-body factors
  4. Correspondence between Grey-Body Factors and Quasinormal Modes
  5. Absorption Cross-Section
  6. Conclusions

Figures (10)

  • Figure 1: Grey-body factors of the scalar field calculated by the 6th order WKB technique and by the correspondence with QNMs (left). The difference between the results obtained by the two methods (right). Here $M=1$, $s=0$, $\ell=0$, $\Lambda =0.7$, $\mu=1$ (blue), $\mu=3$ (red), $\mu=5$ (green); $D=5$.
  • Figure 2: Grey-body factors of the Dirac field calculated by the 6th order WKB technique and by the correspondence with QNMs (left). The difference between the results obtained by the two methods (right). Here $M=1$, $s=1/2$, $\ell=1/2$, $\Lambda=0$ (blue), $\Lambda=0.3$ (red), $\Lambda=0.7$ (green); $D=5$.
  • Figure 3: Grey-body factors of the Dirac field calculated by the 6th order WKB technique and by the correspondence with QNMs (left). The difference between the results obtained by the two methods (right). Here $M=1$, $s=1/2$, $\ell=3/2$, $\Lambda=0$ (blue), $\Lambda=0.3$ (red), $\Lambda=0.7$ (green); $D=5$.
  • Figure 4: Grey-body factors of the electromagnetic field calculated by the 6th order WKB technique and by the correspondence with QNMs (left). The difference between the results obtained by the two methods (right). Here $M=1$, $s=1$, $\ell=1$, $\Lambda=0$ (blue), $\Lambda=0.3$ (red), $\Lambda=0.7$ (green); $D=5$.
  • Figure 5: Grey-body factors of the electromagnetic field calculated by the 6th order WKB technique and by the correspondence with QNMs (left). The difference between the results obtained by the two methods (right). Here $M=1$, $s=1$, $\ell=1$, $\Lambda=0$ (blue), $\Lambda=1$ (red), $\Lambda=2$ (green); $D=6$.
  • ...and 5 more figures