Wiggling Throat of Extremal Black Holes

Understand

We construct the classical phase space of geometries in the near-horizon region of vacuum extremal black holes as announced in [arXiv:1503.07861].

• Motivated by the uniqueness theorems for such solutions and for perturbations around them, we build a family of metrics depending upon a single periodic function defined on the torus spanned by the $U(1)$ isometry directions.
• We show that this set of metrics is equipped with a consistent symplectic structure and hence defines a phase space.
• The phase space forms a representation of an infinite dimensional algebra of so-called symplectic symmetries.