Moduli Spaces of Transverse Deformations of Near-Horizon Geometries

Abstract

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.

Some minor errors in linearized field equations in sections 3 and 4 corrected, with no change to results. Other minor typos removed. 21 pages, latex

References in corpus (3)

• A classification of near-horizon geometries of extremal vacuum black holes
• Einstein--Weyl Spaces and Near-Horizon Geometry
• Anomaly Corrected Heterotic Horizons

Cited by in corpus (6)

• Almost all extremal black holes in AdS are singular
• Supersymmetric near-horizon geometry and Einstein-Cartan-Weyl spaces
• Uniqueness of the extremal Schwarzschild de Sitter spacetime
• Uniqueness of extremal charged black holes in de Sitter
• Non-extremal near-horizon geometries
• Extremal Black Holes from Homotopy Algebras