University of Groningen
The Painlevé VI tau-function of Kerr-AdS5
Barragán Amado, José Julián
DOI:
10.33612/diss.133164493
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Publication date: 2020
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Barragán Amado, J. J. (2020). The Painlevé VI tau-function of Kerr-AdS5. University of Groningen. https://doi.org/10.33612/diss.133164493
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Propositions
accompanying the dissertation
The Painlev´
e VI τ -function of Kerr-AdS
5by
Jos´
e Juli´
an Barrag´
an Amado
1. This thesis focuses on scalar and vector fields propagating in a five-dimensional Kerr-AdS black hole, although the formalism developed here can be used to treat linear perturbations in other space-times as well.
2. The method of isomonodromy relies on the existence of families of Fuchsian systems with the same monodromy data, that can be isomonodromically deformed and lead to the Painlev´e equations.
3. The Painlev´e transcendents solve the connection problem for the Heun type of differ-ential equations, and provide new tools to explore several problems in Mathematics and Physics.
4. A Fuchsian system with four regular singular points can be deformed while preserving its monodromy data. The equations governing the deformation can be reduced to the Painlev´e VI equation. (Chapter 3)
5. The eigenvalue problem of the radial and angular differential equation can be refor-mulated in terms of an initial value problem for the associated Painlev´e VI τ -function. (Chapter 3)
6. An asymptotic expansion for the separation constant can be computed in terms of the angular accessory parameter for slowly rotating or near equally rotating black holes. (Chapter 4)
7. Scalar quasi-normal modes for the s-wave case are stable in the small radius black hole limit. On the other hand, numerical evidence suggests that modes with odd orbital quantum number can develop instabilities for r+ ∼ 10−3. (Chapter 4) 8. Massless vector perturbations on Kerr-AdS5 lead to separable equations through
the introduction of a new parameter µ, which can be associated to the apparent singularity of the isomonodromy method by a M¨obius transformation. (Chapter 5)
