| dc.description.abstract | The nonlinear dynamics of black holes is an increasingly relevant topic of which little
is known. In this thesis, we study the full nonlinear dynamics of black holes, as well as
their linear behavior, and combine them to find a comprehensive picture of the processes
involved. In particular, we study the dynamics of unstable black holes in asymptotically
anti-de Sitter spacetimes. We study their general behavior and approach to the final
equilibrium state. In the first part of this work, we present linear studies of charged
scalar field perturbations of Reissner-Nordstrom anti-de Sitter (RN-AdS) black holes in
the small and large black hole regimes. We present their quasinormal mode spectra, identify
the known mode families—superradiant modes, zero-damped modes, AdS modes, and
the near-horizon mode— and track their migration under variation of the black hole and
field parameters. We present results of the full nonlinear studies of perturbed small and
large RN-AdS, showing the nonlinear development of the unstable superradiant modes.
For generic initial conditions, charge and mass are transferred from the black hole to the
scalar field, until an equilibrium solution with a scalar condensate is reached. Additionally,
we use the results from the linear analysis to construct special initial data corresponding
to an unstable overtone mode. We find that these special data evolve to produce a new
equilibrium state, an excited hairy black hole with the scalar condensate in an overtone
configuration. This state is, however, unstable, and the system eventually decays to the
generic end state. This demonstrates the potential relevance of overtone modes as transients
in black hole dynamics. In the second part of this work, we present linear and
nonlinear studies of a planar Schwarzschild-AdS black hole and two massive scalar fields.
Above the critical energy density the system reaches an equilibrium state where one of the
scalars forms a condensate and the other vanishes. Below the critical energy density, how-
ever, the system displays an instability at the linear regime. We present results of the full
nonlinear development of this instability where a suitable equilibrium condensate does not
exist. Indeed, we present compelling evidence that during the dynamics arbitrarily large
curvatures are uncovered in the vicinity of the horizon, which turn such region singular in
finite time with respect to the boundary observer. | en |
