Higher-derivative corrections to the Kerr quasinormal mode spectrum

We provide the most complete analysis so far of quasinormal modes of rotating black holes in a general higher-derivative extension of Einstein’s theory. By finding the corrections to the Teukolsky equation and expressing them in a simple form, we are able to apply a generalized continued fraction method that allows us to find the quasinormal mode frequencies including overtones. We obtain the leading-order corrections to the Kerr quasinormal mode frequencies of all the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo stretchy="false">(</a:mo><a:mi>l</a:mi><a:mo>,</a:mo><a:mi>m</a:mi><a:mo>,</a:mo><a:mi>n</a:mi><a:mo stretchy="false">)</a:mo></a:math> modes with <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>l</e:mi><e:mo>=</e:mo><e:mn>2</e:mn></e:math>, 3, 4, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mo>−</g:mo><g:mi>l</g:mi><g:mo>≤</g:mo><g:mi>m</g:mi><g:mo>≤</g:mo><g:mi>l</g:mi></g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>n</i:mi><i:mo>=</i:mo><i:mn>0</i:mn></i:math>, 1, 2 and express them as a function of the black hole spin <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>χ</k:mi></k:math> using polynomial fits. We estimate that our results remain accurate up to spins between <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>χ</m:mi><m:mo>∼</m:mo><m:mn>0.7</m:mn></m:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>χ</o:mi><o:mo>∼</o:mo><o:mn>0.95</o:mn></o:math>, depending on the mode. We report that overtones are overall more sensitive to corrections, which is expected from recent literature on this topic. We also discuss the limit of validity of the linear corrections to the quasinormal mode frequencies by estimating the size of nonlinear effects in the higher-derivative couplings. All our results are publicly available in an online repository. Published by the American Physical Society 2024