Moduli Spaces of Transverse Deformations of Near-Horizon Geometries

TL;DR

This paper studies the space of possible small deformations of extremal near-horizon geometries in various theories, showing that these deformations are governed by elliptic PDEs and form a finite-dimensional moduli space.

Contribution

It proves that the moduli space of transverse deformations of near-horizon geometries is finite-dimensional and characterized by elliptic PDE systems in Einstein-Maxwell-Dilaton and D=11 supergravity.

Findings

Deformations are constrained by elliptic PDEs.

Moduli space of deformations is finite-dimensional.

Applicable to Einstein-Maxwell-Dilaton and D=11 supergravity.

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.