Rodrigo Avalos
In this talk, we will analyse a recent notion of energy which is associated to fourth-order gravitational theories and plays an analogous role to that of the classical ADM energy in the context of general relativity. We will first introduce such an energy as conserved quantity canonically associated to perturbations of solutions of the fourth-order space-time equations possessing a time-like Killing field, and then present several of its properties as well as develop some intuitions about it. We will show that, in specific limits, its analysis is tractable and prove positivity and rigidity statements. In particular, in the stationary limit, we will show that the resulting notion of energy is deeply connected to Q-curvature analysis and prove a positive energy theorem which underlies several rigidity phenomena.
