Nonlinear Behavior of Unstable Black Holes in Anti-de Sitter Spacetimes
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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.
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Pablo Bosch Gomez (2020). Nonlinear Behavior of Unstable Black Holes in Anti-de Sitter Spacetimes. UWSpace. http://hdl.handle.net/10012/16369