Greybody Factors for d-Dimensional Black Holes

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 de Sitter and anti-de Sitter (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 de Sitter 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 de Sitter 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).