Grey-body factors and absorption cross-sections of scalar and Dirac fields in the vicinity of dilaton-de Sitter black hole

TL;DR

This work analyzes grey-body factors and absorption cross-sections for massive scalar and massless Dirac fields in the dilaton--de Sitter black-hole background. It derives the master wave equations and effective potentials, then computes grey-body factors using a 6th-order WKB approach and examines their relation to quasinormal modes. The main findings show that increasing the field mass $\mu$ or dilaton charge $Q$ raises the potential barrier and suppresses low-frequency transmission, whereas increasing the cosmological constant $\Lambda$ lowers the barrier and enhances transmission; partial-wave cross-sections exhibit oscillations that smooth out when summed, yielding a total cross-section that transitions from infrared suppression to the geometric capture limit. The results provide a systematic description of scattering and evaporation in dilaton--de Sitter spacetimes and illuminate the validity range of the QNM–GBF correspondence in this context.

Abstract

We investigate the propagation of a massive scalar field and a massless Dirac field in the geometry of a dilaton--de Sitter black hole. Starting from the covariant perturbation equations, we derive the corresponding effective potentials and analyze their dependence on the dilaton charge, field mass, and cosmological constant. Using the WKB approximation, we compute the grey-body factors and study the associated absorption cross-sections. The results show that increasing the field mass or dilaton charge raises the effective potential barrier, leading to a suppression of transmission at low frequencies, while a larger cosmological constant lowers the barrier and enhances transmission. The partial absorption cross-sections for different multipole numbers display the expected oscillatory structure, with the lowest multipoles dominating at small frequencies. After summation over multipoles, the oscillations average out and the total cross-section interpolates between strong suppression in the infrared regime and the geometric capture limit at high frequencies. These findings provide a systematic description of scattering and absorption properties of dilaton--de Sitter black holes for both scalar and fermionic perturbations.

Figures (8)

• Figure 1: Left: Grey-body factors of a scalar field obtained by the 6th order WKB method and via the correspondence with the QNMs for $\Lambda=0.01$, $Q=0.01$, $\ell=0$: $\mu=0$ (blue), $\mu=0.5$ (red), and $\mu=1$ (green). Right: Difference between GBFs obtained by the WKB data via the correspondence for the same values of the parameters.
• Figure 2: Left: Grey-body factors of a scalar field obtained by the 6th order WKB method and via the correspondence with the QNMs for $\Lambda=0.03$, $Q=0.01$, $\ell=0$: $\mu=0.5$ (blue), $\mu=1$ (red), and $\mu=2$ (green). Right: Difference between GBFs obtained by the WKB data via the correspondence for the same values of the parameters. The difference $\Delta \Gamma$ for $\mu=1$ and $\mu=2$ is of the order $10^{-4}$ or smaller and cannot be seen on the plot.
• Figure 3: Left: Grey-body factors of a scalar field obtained by the 6th order WKB method and via the correspondence with the QNMs for $\Lambda=0.03$, $\mu=3$, $\ell=0$: $Q=0.01$ (blue), $Q=0.3$ (red), and $Q=0.6$ (green). Right: Difference between GBFs obtained by the WKB data via the correspondence for the same values of the parameters.
• Figure 4: Left: Grey-body factors of a scalar field obtained by the 6th order WKB method and via the correspondence with the QNMs for $Q=0.1$, $\mu=3$, $\ell=1$: $\Lambda=0.03$ (blue), $\Lambda=0.05$ (red), and $\Lambda=0.07$ (green). Right: Difference between GBFs obtained by the WKB data via the correspondence for the same values of the parameters.
• Figure 5: Left: Grey-body factors of a Dirac field obtained by the 6th order WKB method and via the correspondence with the QNMs for $Q=0.1$, $\mu=3$, $\ell=3/2$: $\Lambda=0.03$ (blue), $\Lambda=0.05$ (red), and $\Lambda=0.07$ (green). Right: Difference between GBFs obtained by the WKB data via the correspondence for the same values of the parameters.