These data are freely available, but if you make use of them for your research please cite
[1] Edgardo Franzin, Stefano Liberati, and Mauro Oi, “Superradiance in Kerr-like black holes”, Phys. Rev. D 103 (2021), 104034. arXiv: 2102.03152.
For a black hole with mass M, spin parameter a and deformation parameter η,
the black-hole event horizon r0 is the largest positive root of r2 − 2Mr + a2 − η/r = 0;
the angular velocity at the horizon is Ω0 = a/(r02 + a2) = a/(2Mr0 + η/r0).
For a given s, l ≥ s and |m| ≤ l.
For each (s, l, m) mode, each Z_s*_l*_m*.dat file contains
| black-hole spin | deformation parameter | wave frequency | amplification factor |
|---|---|---|---|
| a/M | η/M3 | ω M | Zslm |
We give values of a/M = {0.1, …, 0.9, 0.95, 0.96, 0.97, 0.98, 0.99, 0.998, 1., 1.01, …, 1.05, 1.1, 1.15}; for each value of a/M we give values of η/M3 = {η−, …, 0, 0.01, 0.02, …, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, …, 1.}, where η− is defined in Eq. (8) of Ref. [1], and (typically) values of 0 < ω < 2|m|Ω0 for m ≠ 0, and 0 < ω M < 1 otherwise.
For the non-rotating case, i.e. a = 0, the spectra are degenerate in the azimuthal number m, and for each (s, l) mode, each Z_a0_s*_l*.dat file contains
| deformation parameter | wave frequency | absorption factor |
|---|---|---|
| η/M3 | ω M | Zsl |
The file Z_s0_l1_m1_massive.dat contains
| black-hole spin | deformation parameter | mass parameter | wave frequency | amplification factor |
|---|---|---|---|---|
| a/M | η/M3 | M μs | ω M | Z011 |
We give values of a/M = {0., 0.2, …, 0.9, 0.95, 0.96, 0.97, 0.98, 0.99, 0.998, 1., 1.01, …, 1.05, 1.1, 1.15}. For each value of a/M we give values of η/M3 = {η−, …, 0, 0.01, 0.02, …, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, …, 1.}, and M μs = {0.025, 0.05, …} as long as μs < Ω0 and (typically) values of μs < ω < 2 Ω0 − μs.
The Jupyter notebook Plots.ipynb provides several plots in addition to those shown in the paper.
It contains plots for the superradiant modes only, for selected values of the black-hole parameters, but it can be easily modified to visualize other modes and/or other parameter values.
Note. The notebook is rendered better on nbviewer.jupyter.org.
These data include the amplification factor for bosonic waves scattered off a Kerr black hole, i.e. with η = 0.
EF acknowledges partial financial support by CNPq Brazil, process no. 301088/2020-9.
EF and SL acknowledge funding from the Italian Ministry of Education and Scientific Research (MIUR) under the grant PRIN MIUR 2017-MB8AEZ.
MO acknowledges partial financial support by the research project “Theoretical and experimental investigations of accreting neutron stars and black holes”, CUP F71I17000150002, funded by Fondazione di Sardegna.
The authors thankfully acknowledge Daniele Mura for assistance and computer resources provided by INFN, Sezione di Cagliari.