Title: Hamiltonian approach to near extremal black hole physics

Abstract: Much progress has been made in recent years on understanding near-extremal black holes, primarily via the Euclidean path integral. These findings include large backreaction effects at both classical and quantum levels.  However, a Lorentzian formulation of these effects, as needed to describe black holes formed from collapse along with other dynamical processes, is not well understood. I will describe an approach to this problem based on the Hamiltonian formulation of gravity. In this formulation we can make contact with earlier Euclidean results while also generalizing to inherently Lorentzian processes like black hole formation.