Greybody Factors for d-Dimensional Black Holes

TL;DR

This work delivers analytic graviton greybody factors for general $d$-dimensional, static, spherically symmetric black holes, including charged and (A)dS cases, by solving IK master equations and employing both low-frequency matching and high-frequency monodromy methods. It unifies the asymptotically flat, de Sitter, and anti–de Sitter regimes, revealing universal features such as the low-frequency absorption cross-section $oldsymbol{
} o A_H$ for flat spacetimes and the AdS universality $oldsymbol{
} o 1$ at large imaginary frequencies, while exposing rich structure in AdS at low frequencies (e.g., critical and pole-like behavior tied to horizon data and AdS normal modes). The results illuminate how greybody factors encode microscopic and holographic information, connecting black hole emission spectra to horizon geometry, horizon area ratios in dS, and boundary correlators in AdS/CFT, with explicit expressions for Schwarzschild, RN, and their dS/AdS generalizations. The methods—IK master equations, near-horizon matching, and monodromy analysis—provide a coherent framework to study gravitational perturbations across diverse asymptotics and dimensions, offering insights for quantum gravity and holographic applications.

Abstract

Gravitational greybody factors are analytically computed for static, spherically symmetric black holes in d-dimensions, including black holes with charge and in the presence of a cosmological constant (where a proper definition of greybody factors for both asymptotically dS and AdS spacetimes is provided). This calculation includes both the low-energy case --where the frequency of the scattered wave is small and real-- and the asymptotic case --where the frequency of the scattered wave is very large along the imaginary axis-- addressing gravitational perturbations as described by the Ishibashi-Kodama master equations, and yielding full transmission and reflection scattering coefficients for all considered spacetime geometries. At low frequencies a general method is developed, which can be employed for all three types of spacetime asymptotics, and which is independent of the details of the black hole. For asymptotically dS black holes the greybody factor is different for even or odd spacetime dimension, and proportional to the ratio of the areas of the event and cosmological horizons. For asymptotically AdS black holes the greybody factor has a rich structure in which there are several critical frequencies where it equals either one (pure transmission) or zero (pure reflection, with these frequencies corresponding to the normal modes of pure AdS spacetime). At asymptotic frequencies the computation of the greybody factor uses a technique inspired by monodromy matching, and some universality is hidden in the transmission and reflection coefficients. For either charged or asymptotically dS black holes the greybody factors are given by non-trivial functions, while for asymptotically AdS black holes the greybody factor precisely equals one (corresponding to pure blackbody emission).