Quasinormal
modes (QNMs) are the damped vibrations of black hole (BH) spacetimes,
characterising much of the response of a black hole to perturbations. In
Chapter 1, we introduce quasinormal modes, their applications, and ways
to compute them numerically using pseudospectral methods. In
Chapter 2 we study the scalar QNM spectrum of Kerr-Newman. Starting from
the Reissner-Nordström limit, we understand how the spectrum changes as
we vary the ratio of charge to angular momentum, all the way until the
Kerr limit. This clarifies the relationship between the QNM spectra of
Reissner-Nordström and Kerr, and highlights an intricate form of
interaction called eigenvalue repulsion. In asymptotically de
Sitter (dS) spacetimes, an important application of quasinormal modes is
the strong cosmic censorship (SCC) conjecture. In four dimensions,
Christodoulou’s formulation of SCC is violated by charged BHs
(Reissner-Nordström-dS), but holds for rotating BHs (Kerr-dS). In
Chapter 3, we study a higher-dimensional analogue of Kerr-dS, equal
angular momentum Myers-Perry-dS, and show that SCC is respected in odd d
>= 5 dimensions. This suggests that the preservation of SCC in
uncharged rotating black hole backgrounds might be a universal property
of Einstein gravity and not limited to the d = 4 Kerr-dS background. Finally,
in Chapter 4, we construct the static hairy black holes of
Einstein-Maxwell-Scalar theory in a cavity that confines the scalar
field. These hairy black holes are asymptotically flat, with a scalar
condensate floating above the horizon. When they coexist with
Reissner-Nordström BHs, the hairy BHs are thermodynamically preferred,
and hence they are natural candidates for the endpoint of the
superradiant and near-horizon instabilities of the charged black hole
bomb system.