Abstract
Black hole quasinormal modes (QNMs) serve as an indispensable tool in the study of (semi-) classical and
alternative theories of gravity, capable of describing the intricate dynamics of perturbed black hole systems
and of fully characterising their black hole source. Since their identification in the 1970s, QNMs and their
corresponding complex quasinormal frequencies (QNFs) have provided insight into the nature of singularities,
the stability of black hole space-times, and the validity of principles like cosmic censorship and
the no-hair conjecture that pervade general relativity (GR) but remain without formal mathematical proof.
Within the newly-established era of gravitational-wave (GW) astronomy, we can exploit the phenomenological
applications of the extant theoreticalQNMframework; we can performquantitative analyses of GWs
emitted in the wake of black hole merger events and employ these in searches for new physics.
We explore these ideas within this thesis, in the context of fixed spherically-symmetric black hole backgrounds
upon which a scalar test field propagates. In this vein, we seek to understand how parameters
from the black hole space-time and the propagating field influence the QNF spectrum, the constraints we
can derive as a result, and whether QNMs can be used in the search for extra dimensions.
We focus on three space-times in particular: the Schwarzschild black hole, which we choose for its simple
structure; the charged Reissner-Nordström background embedded in an asymptotically-de Sitter spacetime,
which reflects the most complicated spherically-symmetric background with GR; an extra-dimensional
space-time made up of a Schwarzschild black hole embedded in a space-time of mixed curvature.
Within the Schwarzschild space-time, we investigate the influence of a field mass on the scalar QNF
spectrum, where an upper bound can be derived beyond which QNMs fail to propagate. The corresponding
QNFs lie in the quasiresonance regime, related to the phenomenon of superradiance.
As an additional investigation within the Schwarzschild space-time, we extend our analysis of the semiclassical
tools used to compute QNFs to the computation of the QNM wavefunction and “quasinormal excitation
factor” (QNEF). Since tests of GR are mode-specific, QNEFs provide a measurement of relative
excitation required to identify a particular mode within the detected GW spectrum that is independent of
the black hole’s initial perturbing stimulus. In section 2.4, we discuss the procedure we have developed to
construct higher-order QNEFs, based on the Dolan-Ottewill and Schutz-Iyer-Will formalisms.
We then expand our interrogation of the effect of field and black hole parameters on the QNFs by examining
the QNF spectrum of a spin-0 field with mass μ and charge q within the Reissner-Nordström de Sitter
(RNdS) black hole space-time with mass M, charge Q, and cosmological constant Λ > 0. Using a phase
space diagram, we show how the cosmological constant enforces upper limits on the black hole mass and
charge. With this diagram, we review the Weak Gravity Conjecture (WGC) that extracts mass and charge
constraints from black hole mechanics, the Festina-Lente (FL) bound that provides a lower bound of field
mass and charge from black hole decay processes, and the cosmic censorship conjectures that preserve the
deterministic nature of GR.
Through a semi-classical computation method tailored to the calculation of charged and massive scalar
QNMs in the RNdS black hole background, we show how QNFs evolve within the phase space; we demonstrate
regular and anomalous QNF behaviour and its dependence on black hole and field parameters. In
particular, we focus on the application of thisQNManalysis in the study of stability, superradiance, and cosmic
censorship violations within extremised regions of the RNdS black hole. We find regions in the phase
space predisposed to superradiance, as well as QNFs in violation of cosmic censorship.
Our final investigation is focused on the search for signatures of new physics using GWs from binary
black hole collisions. We investigate an extra-dimensional model of mixed curvature whose higher-dimensional
manifold is a compact negative space. Specifically, we are concerned with a product space comprised of a