Advanced topics in GR.
Intended for graduate students on the level of the course NTMF037. Lectures are delivered in English.
The lectures take place on Tuesdays at 16:30 in the lecture hall T1 (big lecture hall close to the main entrance to Troja building). !!! First lecture is on October 8 !!!
Students should choose two topics covered in the course for the examination.
Please contact O. Svítek <ota@matfyz.cz> for more information and/or your selection of topics at the end of semester.
Introduction to scalar-tensor theories, from Horndeski to DHOST models. Bekenstein no hair theorem - Janis-Newman-Winicour spacetime - Buchdahl theorems - Bekenstein transformations and the BBMB black hole. Generalisations of the BBMB and extended conformal frame - No hair in Horndeski theory - The nonminimal derivative coupling sector. Black holes in DHOST with secondary hair - Black holes in beyond Horndeski theory with primary hair.
Definition of cylindrical symmetry. Exact solutions with such a symmetry and their interpretation.
Description of Einstein-Cartan theory in terms of connections. 3+1 splitting of connections.
Killing tensors are associated with hidden symmetries of the phase space. After reviewing the basics of symplectic geometry, and the Eisenhart lift geometrization of Hamiltonian dynamics, we shall discuss the existence of Killing tensors in curved spacetimes, and their applications to spinning tops and classical spinning particles.
© 2021-10-01 Pavel Krtouš <Pavel.Krtous@utf.mff.cuni.cz>