Extremal Rotating Black Holes in the Near-Horizon Limit: Phase Space and Symmetry Algebra

Understand

We construct the NHEG phase space, the classical phase space of Near-Horizon Extremal Geometries with fixed angular momenta and entropy, and with the largest symmetry algebra.

• We focus on vacuum solutions to $d$ dimensional Einstein gravity.
• Each element in the phase space is a geometry with $SL(2,\mathbb R)\times U(1)^{d-3}$ isometries which has vanishing $SL(2,\mathbb R)$ and constant $U(1)$ charges.
• We construct an on-shell vanishing symplectic structure, which leads to an infinite set of symplectic symmetries.