Further clarification on quasinormal modes/circular null geodesics correspondence

@article{76263,
   author = {Konoplya, Roman},
   article_number = {March 2023},
   doi = {http://dx.doi.org/10.1016/j.physletb.2023.137674},
   keywords = {hole normal-modes;black-hole;WBK approach;instability; shadow},
   language = {eng},
   issn = {0370-2693},
   journal = {Physics Letters B},
   title = {Further clarification on quasinormal modes/circular null geodesics correspondence},
   url = {https://www.sciencedirect.com/science/article/pii/S0370269323000084?via%3Dihub},
   volume = {838},
   year = {2023}
}

TY  - JOUR
ID  - 76263
AU  - Konoplya, Roman
PY  - 2023
TI  - Further clarification on quasinormal modes/circular null geodesics correspondence
JF  - Physics Letters B
VL  - 838
IS  - March 2023
SP  - "137674-1"-"137674-2"
EP  - "137674-1"-"137674-2"
SN  - 03702693
KW  - hole normal-modes;black-hole;WBK approach;instability
KW  - shadow
UR  - https://www.sciencedirect.com/science/article/pii/S0370269323000084?via%3Dihub
N2  - The well-known correspondence between quasinormal modes of any stationary, spherically symmetric and asymptotically flat or de Sitter black hole and parameters of the circular null geodesic was initially claimed for gravitational and test field perturbations. According to this correspondence the real and imaginary parts of the Z >> n quasinormal mode (where Z and n are multipole and overtone numbers respectively) are multiples of the frequency and instability timescale of the circular null geodesics respectively. Later it was shown that the correspondence is guaranteed only for test fields and may be broken for gravitational and other non-minimally coupled fields. Here, we further specify the correspondence and prove that even when it is guaranteed, it may not represent the full spectrum of the Z >> n modes, missing the quasinormal frequencies which cannot be found by the standard WKB method. In particular we show that this always happens for an arbitrary asymptotically de Sitter black holes and further argue that, in general, this might be related to sensitivity of the quasinormal spectrum to geometry deformations near the boundaries.
ER  - 

KONOPLYA, Roman. Further clarification on quasinormal modes/circular null geodesics correspondence. \textit{Physics Letters B}. 2023, roč.~838, March 2023, s.~''137674-1''-''137674-2'', 4 s. ISSN~0370-2693. Dostupné z: https://dx.doi.org/10.1016/j.physletb.2023.137674.