Quasinormal Modes in Extremal Reissner–Nordström Spacetimes
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Abstract
We present a new framework for characterizing quasinormal modes (QNMs) or
resonant states for the wave equation on asymptotically flat spacetimes,
applied to the setting of extremal Reissner-Nordstr"om black holes. We show
that QNMs can be interpreted as honest eigenfunctions of generators of time
translations acting on Hilbert spaces of initial data, corresponding to a
suitable time slicing. The main difficulty that is present in the
asymptotically flat setting, but is absent in the previously studied cases of
asymptotically de Sitter or anti de Sitter sub-extremal black hole spacetimes,
is that
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1432-0916