Hairy black holes and other compact objects in theories of gravity

TL;DR

This paper explores alternative theories and matter fields to circumvent the no-hair theorem, analyzing hairy black holes in bigravity, electroweak monopoles, and boson stars, with implications for gravitational wave observations.

Contribution

It introduces new solutions for hairy black holes in bigravity and electroweak theory, and constructs chains of boson stars, expanding understanding of compact objects beyond traditional models.

Findings

Hairy black holes in bigravity can describe stellar and supermassive black holes.

Electroweak monopoles can be regularized within black holes, avoiding singularities.

Chains of boson stars are constructed using finite element methods.

Abstract

In the realm of spacetimes governed by Einstein's general relativity and containing only Maxwell's electromagnetic field, stationary black holes are fully characterized by their mass, electric or magnetic charge, and angular momentum -- a property encapsulated in a version of the no-hair theorem. However, the validity of this theorem is contingent on certain assumptions, and when these are relaxed, new solutions describing hairy black holes arise. To date, astronomical observations have not provided concrete evidence of any type of black hole hair. Nevertheless, the development of increasingly precise gravitational wave detectors has sparked renewed interest in hairy black holes. In this thesis, we delve into two approaches to circumvent the no-hair theorem. The first option consists in describing the spacetime metric by an alternative theory of gravitation. We investigate the dynamical stability of hairy black holes in a vacuum spacetime described by the theory of massive bigravity. We show that hairy black holes in bigravity can describe both stellar black holes and supermassive black holes. The second approach is to keep Einstein's equations but to consider a different material content than Maxwell's electromagnetic field. For this we choose the fields of the electroweak theory. In the absence of gravitation, this theory describes magnetic monopoles with infinite mass. General relativity allows for their regularization by concealing their Coulombian singularity within an event horizon. After providing a detailed analysis of the internal structure of monopoles in flat space, we investigate how their properties generalize to the black hole case. Lastly, we study a particular example of soliton -- boson stars -- arising when a complex scalar field is coupled to general relativity. We construct chains of boson stars by solving the elliptic field equations using the finite element method.