Symmetries and conservation laws in Lagrangian gauge theories with applications to the mechanics of black holes and to gravity in three dimensions

Understand

The treatment of exact conservation laws in Lagrangian gauge theories constitutes the main axis of the first part of the thesis.

• The formalism is developed as a self-consistent theory but is inspired by earlier works, mainly by cohomological results, covariant phase space methods and by the Hamiltonian formalism.
• The thermodynamical properties of black holes, especially the first law, are studied in a general geometrical setting and are worked out for several black objects: black holes, strings and rings.
• Also, the geometrical and thermodynamical properties of a new family of black holes with closed timelike curves in three dimensions are described.