Aspects of four-dimensional black holes with hair : stability and entropy considerations

Thesis

In recent years, a large number of black holes have been presented as candidates for an evasion of the "no-hair" conjecture. These examples typically have two features: a non-Abelian gauge field and instability. A large part of this thesis is devoted to a detailed study of the Einstein-Yang-Mills-Higgs (EYMH) black holes, including the analytic proof of the evasion of the "nohair" theorem in this case and proving that the black holes are unstable. We also consider an example of a "hairy" black hole not involving a non-Abelian gauge field, which arises in a higher derivative model of gravity derived from string theory, and prove analytically how the "no-hair" theorem is evaded.

The rest of this thesis is concerned with the thermodynamics and quantum field theory of these black holes. In a first order approximation to the unknown theory of quantum gravity, we calculate the entropy of the "hairy" black holes. This turns out to be divergent, and parts of the divergences are attributed to the effect of hair on information loss processes occurring as the black hole evolves in time. We pursue this idea further by making a preliminary estimate of the magnitude of the quantum de-coherence effects on the state of the quantum field as time proceeds. These processes may be of interest phenomenologically in the future.

The extension of the theory to non-static geometries is also discussed, by describing the results of bringing rotation into the picture. We prove that the Hartle-Hawking state is not regular everywhere outside the event horizon of a Kerr black hole, with the result that quantum field theory on rotating black hole space-times is more complicated than on static geometries.

Authors: Winstanley, E

• DOI: 10.5287/ora-nrnoqgqzj
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford