Hairy black holes, solitons and multi-oscillators

Abstract

This thesis is centered in the study of new solutions to Einstein’s equations. A common property of all new solutions presented in this thesis is that they have a scalar field condensate, independently of having a horizon or not. A key motivation for studying such cases is given by the gauge/gravity duality hence our starting point will be asymptotically AdS spacetimes. However, we will apply some of the intuition gained from this context to asymptotically flat spacetimes. Within this context, there are two main different parts in this thesis:

♦The study of linear instabilities of charged black holes and the construction of the endpoint of the instabilities: hairy black holes. Firstly, one considers the linear problem of scalar field perturbations in order to characterise the unstable region as well as determining the onset of the instability. This onset is given by a zero-mode perturbation, hence it is regular in the past and future horizons. This zero-mode signals the possible existence of a new solution. Secondly, we solve the non-linear problem using a perturbative expansion and encounter two new solutions in the system: a soliton, which is a horizonless solution and a hairy black hole which is the endpoint of the linear instabilities. This study is performed in asymptotically AdS spacetimes and in asymptotically flat spacetimes with a box at a finite distance with Dirichlet boundary conditions for the scalar field: the black hole bomb.

♦The study of the nonlinear instability of AdS. We present new results in the charactersation of the islands of stability of AdS. In particular we study the dependence of the nonlinear instability on the commensurability of the frequency spectrum of the theory by introducing a double trace deformation in AdS. We study these islands of stability by determining the region of existence of multi-oscillators. In addition, we use the construction as intuition to postulate the existence in asymptotically flat spacetimes of an infinite-parameter family of solutions that oscillate on any number of non-commensurate frequencies. A particular solution within this infinite-parameter family is the well-known boson star solution which oscillates in one frequency. We construct numerically two-frequency solutions: double-oscillators.

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Identifiers

ORCID for Oscar Campos Dias: orcid.org/0000-0003-4855-4750

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