The topic of this thesis is the dynamics of black holes.

In a close to equilibrium, or late time, approximation, these dynamics are given in terms of damped oscillations called quasinormal modes (QNMs). A given black hole allows only a discrete set of oscillation frequencies and corresponding decay rates.

We developed a computer code to compute to compute these numerically in a quite general setting.

This is then applied to various physical questions.

First, within the theory of General Relativity (GR) there is the Strong Cosmic Censorship (SCC) conjecture, which conjectures that Cauchy horizons, beyond which GR cannot predict a unique evolution, do not exist within a generic black hole. For charged black holes in de Sitter spacetime, the validity of this conjecture relies crucially on the decay rate of fluctuations, the QNMs. By computing these we find indications that the conjecture is violated for black holes in de Sitter with near extremal charge.

The other applications are all in the context of holography, which relates the physics of black holes in anti de Sitter spacetime to that of strongly coupled quantum field theories in one dimension less.

We study the effect of perturbations on the size of the event horizon of a black hole, which is dual to the entropy of the fluid that is described by the dual quantum field theory. This area can never decrease, by a theorem in GR which is dual to the second law of thermodynamics. It is found however that this second law is saturated: the entropy oscillates as much as it can given the second law, meaning that while it never decreases, there are moments in time where it is constant.

Going beyond the late time approximation one has to solve the full nonlinear Einstein equations, which allows one to study the thermalization of strongly coupled fluids. We adapt the standard formalism to do this in holography from the default relativistic fluids to nonrelativistic ones. Similar to the relativistic case we find that the evolution is surprisingly well described by a sum of quasinormal modes, even for initial conditions far from equilibrium. Thermalization occurs in the order of the inverse temperature. The order one coefficient depends on the dynamical scaling exponent z that controls the scaling of energy with momentum, in a way that is well predicted by the QNMs.

Finally we study a different theory that is inspired by QCD, in particular it is non-conformal and confining at low energies. While the theory under consideration seems a priori perfectly well defined, we observe very peculiar behavior. There is a dynamical instability, in a phase which is thermodynamically stable. Furthermore, this dynamically unstable state can evolve to a dynamically stable state, but there is a different possibility. Instead it can keep increasing its horizon area, never reaching a new equilibrium but reaching the anti de Sitter boundary in finite time.