Seminář se koná v úterý ve 13:10 v posluchárně ÚTF MFF UK
v 10. patře katedrové budovy v Tróji, V Holešovičkách 2, Praha 8
I will discuss spacetime symmetries that enable consistent symmetry reductions of gravitational Lagrangians, fully recovering the reduced field equations for any four-dimensional metric theory of gravity. After reviewing the principle of symmetric criticality (PSC), I will present the PSC-compatible symmetries, symmetry-invariant metrics and l-chains; analyze mutual relations of symmetries and examples of known GR solutions; and address simplifications of the reduced Lagrangians allowed by residual diffeomorphisms (via Noether identities). As an application, I will show how symmetry reduction can be used to construct non-polynomial quasi-topological theories exhibiting GR-like integrability of the field equations across a broad class of symmetries, including those of spherical, hyperbolic, and planar Schwarzschild and Taub–NUT, B-metrics, near-horizon extreme Kerr, and the swirling universe, and which admit exact closed-form solutions in these cases.
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.
David Kubizňák Oldřich Semerák