Ponglertsakul, Supakchai (2016) Aspects of selfgravitating solitons and hairy black holes. PhD thesis, University of Sheffield.

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Abstract
This thesis considers two particular systems of gravity coupled to matter: EinsteinnonAbelianProca (ENAP) theory with gauge group $SU(2)$ in asymptotically antide Sitter (AdS) spacetime and Einsteinchargedscalar theory in a cavity. The first part of this thesis is devoted to the ENAPAdS model. For a purely magnetic gauge field we obtain spherically symmetric solitons and black holes with nonAbelian Proca hair. This is achieved by solving the corresponding field equations numerically. We prove that the equilibrium gauge field must have at least one node. Then we turn to dyons and dyonic black holes which carry both electric and magnetic charge. We show that no nontrivial dyons or dyonic black holes exist in this model. We perturb the equilibrium solutions under linear, spherically symmetric perturbations of the metric and gauge field. We find numerical evidence which reveals that the solitons and hairy black holes are linearly unstable. These hairy black holes violate the generalized nohair conjecture in the sense that they look identical to the SchwarzschildAdS metric when observed from infinity. In the second part of this thesis, we investigate a plausible endpoint of the charged superradiant instability. We study the EinsteinMaxwellKleinGordon (EMKG) equations with a mirrorlike boundary condition. We construct numerical solitons and black holes with charged scalar hair. Then we study the stability of the equilibrium solutions under linear, spherically symmetric perturbations of the metric, electromagnetic and scalar fields. When the mirror is located at the first zero of the static scalar field, we find stable solitons if the mirror radius is sufficiently large. However when the mirror radius is sufficiently small, some solitons are found to be unstable. In the black hole case, we find no evidence of instability when the mirror is located at the first zero of the static scalar field. In contrast, numerical evidence shows that the hairy black holes are unstable if the mirror is located at the second zero of the static scalar field. We conclude that these stable hairy black holes could represent an endpoint of the charged superradiant instability.
Item Type:  Thesis (PhD) 

Academic Units:  The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) 
Identification Number/EthosID:  uk.bl.ethos.693101 
Depositing User:  Mr. Supakchai Ponglertsakul 
Date Deposited:  02 Sep 2016 15:43 
Last Modified:  03 Oct 2016 13:19 
URI:  http://etheses.whiterose.ac.uk/id/eprint/13814 