Emanuele Berti bio photo

Emanuele Berti

Associate Professor, University of Mississippi

Email Facebook Google+

Ringdown

The oscillation modes of black holes are called “quasinormal modes” (QNMs; “quasi” because they are damped by the emission of gravitational radiation). These quantities are of interest in gravitational-wave astronomy, to test the so-called “no-hair theorem” of general relativity, and in the context of the gauge-gravity duality. Here you can find data for:

  • the QNM spectrum of Schwarzschild (anti-de Sitter) and Kerr black holes.
  • the excitation factors of Kerr quasinormal modes.
  • the spherical-spheroidal mixing coefficients between the angular functions that correspond to each mode (spin-weighted spheroidal harmonics) and the spin-weighted spherical harmonics normally used to decompose gravitational radiation.

You can also find Mathematica notebooks to compute some of these quantities. The data and routines are freely available, but please reference the original work(s). Important caveat: the calculations of Kerr QNM frequencies presented here are unreliable very close to the Kerr extremal limit (roughly, when ). The near-extremal regime is discussed in arXiv:1212.3271 and arXiv:1307.8086; see also arXiv:1410.7698.

I would like to thank Oscar Dias, Mahdi Godazgar and Jorge Santos for providing Kerr-Newman quasinormal mode data from arXiv:1501.04625.

Description Reference(s) Download  
Schwarzschild QNM frequencies arXiv:0905.2975  
Data format: gr-qc/0512160  
, error,    
Kerr QNM frequencies () arXiv:0905.2975  
Data format: gr-qc/0512160  
   
     
     
     
Kerr QNM frequencies () arXiv:0905.2975  
Data format: gr-qc/0512160  
   
     
     
     
     
Kerr QNM frequencies () arXiv:0905.2975  
Data format: gr-qc/0512160  
   
     
     
     
     
     
Fits to Kerr QNM frequencies arXiv:0905.2975 dat  
gr-qc/0512160    
     
     
Calculation of Kerr QNMs arXiv:0905.2975 Notebook  
using Leaver’s method gr-qc/0512160    
Calculation of Schwarzschild-AdS QNMs arXiv:0905.2975 Notebook  
using power-series methods      
Proca field on a Kerr background arXiv:1209.0465 Notebook  
at second order in a slow-rotation expansion arXiv:1209.0773    
Gravito-EM Kerr-Newman perturbations arXiv:1304.1160 Notebook  
at first order in a slow-rotation expansion arXiv:1304.1160    
Kerr-Newman gravitational QNMs arXiv:1501.04625  
Data format: ()      
     
Kerr excitation factors arXiv:1305.4306 Notebook  
Data format:    
   
   
Spherical-spheroidal mixing coefficients arXiv:1408.1860  
Gravitational case ()    
Data format:    
   
     
     
    Fits  
    Readme  
Spherical-spheroidal mixing coefficients arXiv:1408.1860  
Electromagnetic case ()    
Data format:    
   
     
     
     
Spherical-spheroidal mixing coefficients arXiv:1408.1860  
Scalar case ()    
Data format:    
   
     
     
     
     
Spheroidal-spheroidal mixing coefficients arXiv:1408.1860  
Gravitational case ()    
Data format:    
   
     
     
    Fits  
    Readme