Grey-body factors for gravitational and electromagnetic perturbations around Gibbons-Maeda-Garfinkle-Horovits-Strominger black holes

While grey-body factors for a test scalar field in stringy black holes described by the renowned Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) solution have been analyzed in the literature, no such analysis exists for gravitons, likely due to the complexity of the perturbation equations. In this study, we utilize known data on quasinormal modes and the relationship between quasinormal modes and grey-body factors to derive these factors for gravitational and electromagnetic perturbations of the dilaton black hole. Our findings indicate that grey-body factors are significantly suppressed by the dilaton parameter as the black hole’s charge approaches its extreme value. The iso-spectrality between axial and polar channels of perturbations is broken in the presence of the dilaton field, which leads to different grey-body factors for different types of perturbations.

💡 Research Summary

The paper addresses a gap in the literature concerning the grey‑body factors of gravitational and electromagnetic perturbations of the Gibbons‑Maeda‑Garfinkle‑Horowitz‑Strominger (GMGHS) dilaton black hole, a solution that arises in the low‑energy limit of heterotic string theory. While scalar field grey‑body factors have been studied, the coupled graviton‑photon‑dilaton system has resisted analytic treatment because the perturbation equations are highly intricate. The author exploits a recently established correspondence between quasinormal modes (QNMs) and grey‑body factors, which is exact in the eikonal limit and accurate for moderate multipole numbers, to bypass the direct solution of the wave equations.

The GMGHS metric is presented with the dilaton coupling parameter a (set to a = 1 for the string‑theoretic case). The outer and inner horizon radii r₊ and r₋ encode the mass M and electric charge Q. Perturbations separate into axial (two coupled potentials V₁ᵃ, V₂ᵃ) and polar (three coupled potentials V₁ᵖ, V₂ᵖ, V₃ᵖ) sectors, each reducible to Schrödinger‑like equations for the master variables Ψᵢ. The polar potentials are so cumbersome that they have not been written explicitly in the literature, but their QNM spectra have been computed numerically in earlier works (references