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

Abstract

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-Nordström 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-Nordström 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.

Greybody factors for Myers–Perry black holes

“…(29) Note that the equivalent result for n = 0 was already derived in Ref. 11 for the Kerr-Newman spacetime. Second, for n ≥ 0, we also have n(n − 2) (r ) 4r 2 + n (r ) 2r ∝ n{(n − 2) (r ) + 2r (r )} = n{(n + 2)r 2 + (n − 2)a 2 + nμr 1−n }.…”

“…Furthermore, the separation constant and effective potential reduce to those discussed in Ref. 11. Ultimately, the bounds on the greybody factors reduce (as they should) to those of Ref.…”

“…11. These spheroidal harmonics are very closely related both to the Heun functions, [39][40][41][42] and to the hyper-spherical harmonics.…”

“…44 and 45, while a specific analysis closely related to the current situation can be found in Ref. 11. The key point is that superradiance is a phenomenon in which the reflected wave is larger in its amplitude than the incident wave.…”

“…7 In view of this difficulty, techniques for placing analytic bounds on the greybody factors have now become of some interest. [7][8][9][10][11] (Alternatively, one might seek to extract qualitative or numerical information. [12][13][14] The bounds developed in Refs.…”