Hamiltonian analysis of the Einstein’s equations in General Relativity

The research project aims to develop a covariant Hamiltonian description of the gravitational interaction and to analyze the geometric properties of Einstein's equations for general relativity on non-globally hyperbolic manifolds. The activity focuses on three main points: 1. Global analysis of the pre-symplectic algorithm for the Palatini formulation of Einstein's equations; 2. Geometric characterization of gauge symmetries as the kernel of the pre-symplectic form; 3. Study of the quotient space geometry.