Abstract
We present new analytic results on black hole perturbation theory. Our results are based on a novel relation to four-dimensional {mathcal {N}}=2 supersymmetric gauge theories. We propose an exact version of Bohr-Sommerfeld quantization conditions on quasinormal mode frequencies in terms of the Nekrasov partition function in a particular phase of the Omega -background. Our quantization conditions also enable us to find exact expressions of eigenvalues of spin-weighted spheroidal harmonics. We test the validity of our conjecture by comparing against known numerical results for Kerr black holes as well as for Schwarzschild black holes. Some extensions are also discussed.
Highlights
Finding analytic solutions in spectral theory of quantum mechanical operators is hard
It is recently recognized that a geometric perspective of spectral theory [1,2] often provides us with many useful tools, developed in supersymmetric gauge theories [3,4,5,6] and topological string theory [7,8], to obtain exact solutions for new families of quantum spectral problems
We find that quasinormal modes (QNMs) frequencies of these black holes are determined by Bohr-Sommerfeld-type quantization conditions in SU (2) SW theory with three fundamental hypermultiplets (Nf = 3)
Summary
Finding analytic solutions in spectral theory of quantum mechanical operators is hard. We point out in this work that these spectral problems can be “solved” by using four-dimensional supersymmetric gauge theories in a particular phase of the Ω-background [15,16]. The extremal limit of the Kerr black holes turns out to correspond to the decoupling limit in SW theory, where one of the masses is sent to infinity and we are left with two fundamental hypermultiplets (Nf = 2) This kind of quantization conditions has already been proposed in [19] for Schwarzschild black holes in the complex WKB approach. We find an explicit expression of the angular eigenvalues, see Eq (4.16), and we propose an exact quantization condition for the radial Teukolsky equation, see Eq (4.18) for the generic situation and Eq (4.19) for the extremal limit. In Appendix A we recall the definition of the NS free energy
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
