  Finding exact solutions for black-hole greybody factors is generically
impractical; typically one resorts either to making semi-analytic or numerical
estimates, or alternatively to deriving rigorous analytic bounds. Indeed,
rigorous bounds have already been established for the greybody factors of
Schwarzschild and Riessner-Nordstrom black holes, and more generally for those
of arbitrary static spherically symmetric asymptotically flat black holes.
Adding rotation to the problem greatly increases the level of difficulty, both
for purely technical reasons (the Kerr or Kerr-Newman black holes are generally
much more difficult to work with than the Schwarzschild or Reissner-Nordstrom
black holes), but also at a conceptual level (due to the generic presence of
super-radiant modes). In the current article we analyze bounds on the greybody
factors for scalar excitations of the Kerr-Newman geometry in some detail,
first for zero-angular-momentum modes, then for the non-super-radiant modes,
and finally for the super-radiant modes.
