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The well-known duality 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 duality the real
and imaginary parts of the $\ell \gg n$ quasinormal mode (where $\ell$ 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 duality is guaranteed only for test fields and may be broken
for gravitational and other non-minimally coupled fields. Here, we farther
specify the duality and prove that even when the duality is guaranteed it may
not represent the full spectrum of the $\ell \gg n$ 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.

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