Greybody factors for rotating black holes in higher dimensions

We perform a thorough study of greybody factors for minimally-coupled scalar fields propagating on the background of rotating black holes in higher (odd) dimensions with all angular momenta set equal. For this special case, the solution enjoys an enhanced symmetry, which translates into the advantageous feature of being cohomogeneity-1, i.e., these backgrounds depend on a single radial coordinate. Our analysis contemplates three distinct situations, with the cosmological constant being zero, positive or negative. Using the technique of matched asymptotic expansions we compute analytically the greybody factors in the low-frequency regime, restricting to s-wave scattering. Our formulas generalize those obtained previously in the literature for the static and spherically symmetric case, with corrections arising from the change in the horizon area due to rotation. It is also proven that, for this family of black holes, the horizon area is a decreasing function of the spin parameter, without regard of dimensionality and of cosmological constant. Through an improvement on a calculation specific to the class of small black holes in anti-de Sitter and not restricted to the usual low-frequency regime, we uncover a rich structure of the greybody spectrum, more complex than previously reported but also enjoying a certain degree of universality. We complement our low-frequency analytic results with numerical computations valid over a wide range of frequencies and extend them to higher angular momentum quantum numbers, $\ell>0$. This allows us to probe the superradiant regime that is observed for corotating wavefunctions. We point out that the maximum amplification factor for intermediate-size black holes in anti-de Sitter can be surprisingly large.