Bounding the greybody factors for scalar field excitations on the Kerr-Newman space time

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 field excitations on 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.