The thesis derives explicit first integrals and Killing tensors for geodesics in near-horizon Myers-Perry black holes, introduces a B-memory formulation of gravitational memory, and constructs resonant spacetimes from superintegrable quantum systems.
The missing top of AdS resonance structure
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abstract
We study a massless scalar field in AdS_{d+1} with a nonlinear coupling \phi^N and not limited to spherical symmetry. The free-field-eigenstate spectrum is strongly resonant, and it is commonly believed that the nonlinear coupling leads to energy transfer between eigenstates. We prove that when $Nd$ is even, the most efficient resonant channels to transfer energy are always absent. In particular, for N=3 this means no energy transfer at all. For N=4, this effectively kills half of the channels, leading to the same set of extra conservation laws recently derived for gravitational interactions within spherical symmetry.
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Integrable systems connected with black holes
The thesis derives explicit first integrals and Killing tensors for geodesics in near-horizon Myers-Perry black holes, introduces a B-memory formulation of gravitational memory, and constructs resonant spacetimes from superintegrable quantum systems.