Boundary conditions and energy in general relativity

Simone Speziale

Even though general relativity lacks a notion of local energy density, Noether theorem can be used to single out a quasi-local energy in many situations of physical interest. In non-radiative spacetimes, this energy can be shown to be a canonical Hamiltonian generator of symmetries. However, we show that its explicit form depends on the choice of boundary conditions, thus adding a new layer of non-universality of gravitational energy. In the radiative case, the symplectic form is not conserved, and one needs a prescription to define the energy. This was provided by Wald-Zoupas ’99, and we discuss some recent developments concerning this construction, discussing what boundary conditions is related to, and allowing for a comparison of surface charges at future null infinity and on finite null hypersurfaces.