Moduli spaces of transverse deformations of near-horizon geometries

We investigate deformations of extremal near-horizon geometries in Einstein–Maxwell–Dilaton theory, including various topological terms, and also in D   =  11 supergravity. By linearizing the field equations and Bianchi identities over the compact spatial cross-sections of the near-horizon geometry, we prove that the moduli associated with such deformations are constrained by elliptic systems of PDEs. The moduli space of deformations of near-horizon geometries in these theories is therefore shown to be finite dimensional. (paper)