Abstract
The aim of this thesis is to present the method of isomonodromic deformations to treat linear perturbations of matter fields propagating in a five dimensional KerrAdS black hole. Yet, the method applies to different spacetimes, as well as other physical systems.
The KleinGordon equation leads to radial and angular second order ordinary differential equations with four regular singular points. The associated Fuchsian system can be deformed while preserving its monodromy data, where the isomonodromic equations reduce to the Painlevé VI (PVI) equation, with a consistent definition of the PVI taufunction.
By means of the taufunction we can reformulate the eigenvalue problem of the radial (angular) Heun equation into an initial value problem of the corresponding taufunction. An asymptotic expansion for the separation constant is computed in terms of the angular PVI taufunction for slowly rotating or nearequally rotating black hole, while the quasinormal modes frequencies are found in the small radius limit.
Scalar quasinormalmodes for the swave case and even orbital quantum number turn out to be stable for small black holes. Instead, modes with odd orbital quantum number do exhibit a regime of superradiance in the this limit.
Furthermore, we consider vector perturbations in this background, where the separability of the Maxwell equations comes at the expense of the introduction of a new parameter mu, which can be associated to the apparent singularity of the isomonodromy method by a Möbius transformation. Finally, a numerical analysis is performed for QNMs in the ultraspinning limit.
The KleinGordon equation leads to radial and angular second order ordinary differential equations with four regular singular points. The associated Fuchsian system can be deformed while preserving its monodromy data, where the isomonodromic equations reduce to the Painlevé VI (PVI) equation, with a consistent definition of the PVI taufunction.
By means of the taufunction we can reformulate the eigenvalue problem of the radial (angular) Heun equation into an initial value problem of the corresponding taufunction. An asymptotic expansion for the separation constant is computed in terms of the angular PVI taufunction for slowly rotating or nearequally rotating black hole, while the quasinormal modes frequencies are found in the small radius limit.
Scalar quasinormalmodes for the swave case and even orbital quantum number turn out to be stable for small black holes. Instead, modes with odd orbital quantum number do exhibit a regime of superradiance in the this limit.
Furthermore, we consider vector perturbations in this background, where the separability of the Maxwell equations comes at the expense of the introduction of a new parameter mu, which can be associated to the apparent singularity of the isomonodromy method by a Möbius transformation. Finally, a numerical analysis is performed for QNMs in the ultraspinning limit.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  30Sept2020 
Place of Publication  [Groningen] 
Publisher  
DOIs  
Publication status  Published  2020 