Quasinormal mode/grey-body factor correspondence for Kerr black holes

Abstract

We establish a quasinormal-mode/grey-body factor correspondence for Kerr black holes in the eikonal limit. By recasting the radial Teukolsky equation into a Schrödinger-type form with a short-range potential, we derive WKB connection formulas that relate Kerr quasinormal frequencies to grey-body transmission coefficients. Higher-order WKB corrections are included, extending the correspondence beyond the leading eikonal regime. For gravitational perturbations, the predicted grey-body factors agree with numerical results obtained from the generalized Sasaki-Nakamura equation, with increasing accuracy at large angular quantum number. The correspondence breaks down in the superradiant regime, where the WKB assumptions fail.

Figures (6)

• Figure 1: Different regions for the radial wavefunction. The WKB analysis is valid in regions I and III. The near-peak region is located at II.
• Figure 2: Left: Exact GBFs (black lines) and the approximations by QNM/GBF correspondence (colored lines) of the gravitational perturbations for Kerr BHs with $a=0.3,0.6,0.9$ (left to right) for $l=2$ and $m=0$. Right: The difference between the exact values and the approximations for the same values of the parameters.
• Figure 3: Left: Exact GBFs (black lines) and the approximations by QNM/GBF correspondence (colored lines) of the gravitational perturbations for Kerr BHs with $a=0.25,0.50,0.75,0.99$ (left to right) for the $l=m=2$ mode. Right: The difference between the approximate and the exact values of the GBFs.
• Figure 4: Left: Exact GBFs (black lines) and the approximations by the correspondence (colored lines) of the gravitational perturbations for Kerr BHs with $a=0.8$ for $l=2$ and $m=-2,-1,0,1,2$ (left to right). Right: Difference between the approximate and the accurate values of the GBFs.
• Figure 5: GBFs of a Kerr BH for $a=0.8, s=-2, l=m=2$, negative values due to superradiance.