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.
Invariants of the spherical sector in conformal mechanics
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abstract
A direct relation is established between the constants of motion for conformal mechanics and those for its spherical part. In this way we find the complete set of functionally independent constants of motion for the so-called cuboctahedric Higgs oscillator, which is just the spherical part of the rational A_3 Calogero model (describing four Calogero particles after decoupling their center of mass).
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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.