Two-Center Black Holes Duality-Invariants for stu Model and its lower-rank Descendants

Understand

We classify 2-center extremal black hole charge configurations through duality-invariant homogeneous polynomials, which are the generalization of the unique invariant quartic polynomial for single-center black holes based on homogeneous symmetric cubic special Kaehler geometries.

• A crucial role is played by an horizontal SL(p,R) symmetry group, which classifies invariants for p-center black holes.
• For p = 2, a (spin 2) quintet of quartic invariants emerge.
• We provide the minimal set of independent invariants for the rank-3 N = 2, d = 4 stu model, and for its lower-rank descendants, namely the rank-2 st^2 and rank-1 t^3 models; these models respectively exhibit seven, six and five independent invariants.