# Black hole ringdown, and theoretical considerations concerning k-essence, Rastall and entangled gravity

Name: Edison Cesar de Oliveira Santos

Type: PhD thesis

Publication date: 24/09/2021

Advisor:

Name | Role |
---|---|

Júlio César Fabris | Advisor * |

Examining board:

Name | Role |
---|---|

Wiliam Santiago Hipolito Ricaldi | Internal Examiner * |

Vilson Tonin Zanchin | External Examiner * |

Riccardo Sturani | Internal Examiner * |

Osvaldo Mario Moreschi | External Examiner * |

Odylio Denys de Aguiar | External Examiner * |

Nelson Lloyd Christensen Jr. | External Examiner * |

Summary: While the detection of gravitational waves was an outstanding achievement in theo- retical and observational physics, data science, computer science and engineering on their own merit, it also allowed us to observe black holes for the first time. Black hole physics had a tumultuous research history, from a nearly non-existent field to work, in the first years of general relativity, culminating in the golden age of general relativity in the sixties and mid-seventies, WHERE black holes entered the mainstream theoretical physics. We could be arguably living in the second golden age of general relativity, but this time around black holes entered the mainstream observational physics. In light of this, this thesis tackle some problems in black hole physics, or in a broader sense, the current understanding of gravity. The first part of this thesis is devoted to developing the machinery of first-order perturbation theory in order to obtain the quasi-normal modes from both singular and non-singular black holes, that is, the frequencies related to the oscillation of a black hole after its merging. In the next section we contrast how a particular analytical model, that works from the merger up to the ringdown phase, constrains both the final mass and spin parameter when compared to the published results. In the second part, we investigate a series of works related to spherically-symmetric solutions of both k-essence and Rastall theories, WHERE a possible solution to what seems a coincidence in both theories, might be related to a formulation of a lagrangian formalism for the latter theory. We end this thesis finding black hole solutions to a novel theory of gravity, entangled gravity. This model is not defined in the absence of any matter field, but we argue that black hole solutions satisfying the near vacuum condition resembles solutions obtained in standard general relativity.