  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).
