Quasinormal modes of rapidly rotating black holes/ Stability of tidally perturbed neutron stars

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will review recent work in two very different topics. First, I will discuss the
quasinormal mode spectrum of nearly extremal Kerr black holes, where a
bifurcation of the frequency spectrum is observed. In addition, collective
oscillations of many modes is possible, resulting in a power-law rather than
exponentially decaying ringdown. Next, I will discuss a recent proposal for how
tidally induced, multimode coupling of normal modes in neutron stars can
destabilize the stars. Such an instability could hamper gravitational wave
detection of neutron star binaries by matched filtering. By accounting for
higher-order multimode couplings, it can be shown that there is no such
instability for neutron star binaries, although a milder instability may exist
for binaries with less compact objects.