Thesis

Uniqueness theorems for black holes with matter possessing a harmonic time dependence

• Call:

  IDPASC Portugal - PHD Programme 2016

• Academic Year:

  2016 / 2017

• Domains:

  General Relativity | Astrophysics

• Supervisor:

  Filipe Mena

• Co-Supervisor:

  Carlos Herdeiro

• Institution:

  Universidade do Minho

• Host Institution:

  U. Minho and U. Aveiro

• Abstract:

  Black holes and boson stars play an important role in several astrophysical processes, including in the evolution of stars and galaxies, being sources of gravitational waves. Central aspects to the physics of black holes are the uniqueness theorems which tell us that the unique vacuum solution to the Einstein Field Equations with a regular, stationary asymptotically flat black hole is the Kerr solution. This result was summarised by J. Wheeler in the phrase "black holes have no hair". However, this paradigm should be reconsidered taking into account recent results which say that scalar or vector massive fields, with a harmonic time dependence that, nevertheless, vanishes at the level of the energy momentum tensor, can give rise to "hair" for Kerr black holes. An important question is now to understand what are the most general black hole solutions in these models and, in particular, if one can prove that, for instance, in massive-scalar-vacuum, the hairy black holes obtained thus far are the most general solutions. The first goal of this thesis is to generalize the uniqueness theorems established for electrovacuum to these models. Hairy black holes, as well as some very compact stars, are examples of spacetimes containing a so-called ergo-region which can lead to an instability. The second goal of the thesis is to study the stability of general spacetimes with ergo-regions.