Greybody factors of string-corrected d-dimensional black holes

TL;DR

Greybody factors quantify the deviation of Hawking radiation from a pure blackbody due to curvature scattering. The paper derives analytic expressions for these factors in string-corrected $d$-dimensional black holes in two high-frequency limits: the eikonal regime, with large real part of $\omega$, and the highly damped regime with large $|\mathrm{Im}(\omega)|$. Employing a WKB analysis for eikonal modes and a monodromy approach for highly damped frequencies, they obtain a universal leading factor $\gamma_0(\omega)$ and perturbative string corrections $\lambda'$ such that $\gamma(\omega)=\gamma_0(\omega)\left(1+\lambda'\delta\gamma(\omega)\right)$; explicit closed forms for $\delta\gamma(\omega)$ are provided separately for tensorial gravitational perturbations and for test scalar fields, with dimension-dependent constants $\rho_g,\rho_s$ and phase factors. In the asymptotic regime, a comparable structure appears, with $\gamma_0(\omega)=\dfrac{e^{\omega/T_{\mathcal{H}}}-1}{e^{\omega/T_{\mathcal{H}}}+3}$ and $\delta\gamma_g(\omega)$ or $\delta\gamma_s(\omega)$ encoding the $\alpha'$ corrections through gamma-function factors that depend on the spacetime dimension $d$. The results offer analytic benchmarks for string-corrected black holes and inform Hawking spectra and possible phenomenology in higher-dimensional/string-inspired gravity.

Abstract

We compute analytically greybody factors for asymptotically flat spherically symmetric black holes with stringy higher derivative corrections in d dimensions in the high frequency limit. Our calculations include both the eikonal limit - where the real part of the frequency of the scattered wave is much larger than the imaginary part - and the highly damped case - where the imaginary part of the frequency is much larger than the real part -, addressing the emission of gravitons and test scalar fields, and yielding full transmission and reflection scattering coefficients.

Figures (5)

• Figure 1: Plot of the metric function $f(r)$ for different dimensions and values of $\lambda'$. The horizontal axis stands for $r/R_H$.
• Figure 2: Plot of the potential $V_{\textsf{min}} [f(r)]$ for different dimensions and values of $\lambda'$. The horizontal axis stands for $r/R_H$.
• Figure 3: Plot of the potential $V_{\textsf{T}} [f(r)]$ for different dimensions and values of $\lambda'$. The horizontal axis stands for $r/R_H$.
• Figure 4: Schematic depiction of the big contour, as the blue dashed line. Red curves are Stokes lines. Furthermore, we marked by $D$ and $U$ the regions where the boundary condition (\ref{['130']}) may be imposed.
• Figure 5: Schematic depiction of the small and big contours as the orange and blue dashed lines respectively. The orange contour is to be interpreted as arbitrarily close to $R_H$. Red curves are Stokes lines.