Quasinormal modes, strong cosmic censorship and instabilities

Abstract

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.

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