Seminar is held on Tuesdays at 13:10 pm in the lecture room of the Institute
on the 10th floor of the department building at Trója, V Holešovičkách 2, Prague 8
The motion of spinning test particles in curved space-time is a classical relativistic problem. Astrophysically, the model captures the leading spin-orbital coupling influencing the motion of rotating compact objects. Consequently, solving the equations of motion of spinning particles in black hole space-times to linear order in spin provides information used in the modelling of extreme mass ratio inspirals. To leading order, the spin of the particle is parallel transported, and this feeds into the equations of motion of the particle. Thus, it was already known that separable parallel transport made the problem much more tractable, even though we struggled to incorporate this usefully in the Hamiltonian formalism. Here we end those struggles and end up proving the following theorem: if parallel transport in a space-time is separable, then so is the motion of spinning test particles to linear order in spin.
I will describe a new construction of Ricci flat metrics using gauged linear sigma models satisfying the Calabi-Yau condition. The approach will be introductory using elementary examples to illustrate the main points and to underline the connection between physical and mathematical concepts.
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David Kubizňák Oldřich Semerák