Charged Dilatonic Spacetimes in String Theory

TL;DR

This paper constructs and analyzes a broad class of static, magnetically charged solutions in Einstein-Maxwell-dilaton gravity, revealing new warped geometries and detailed near-horizon behaviors relevant to string theory and Kaluza-Klein models.

Contribution

It introduces a three-parameter family of solutions generalizing known black holes, including detailed near-horizon analysis and linearized solutions in specific limits.

Findings

Discovery of new warped geometries near extremality

Characterization of horizon perturbations and their nonlinear completions

Extension of known black hole solutions to more general dilaton couplings

Abstract

We construct and study general static, spherically symmetric, magnetically charged solutions in Einstein-Maxwell-dilaton gravity in four dimensions. That is, taking Einstein gravity coupled to a ${\rm U}(1)$ gauge field and a massless dilaton$\unicode{x2014}$e.g., the action in the low-energy limit of string theory or Kaluza-Klein reduction$\unicode{x2014}$with arbitrary dilaton coupling, we build a three-parameter family of objects characterized by their mass, charge, and dilaton flux, generalizing the well known Garfinkle-Horowitz-Strominger black hole. We analyze the near-extremal and near-horizon behavior in detail, finding new warped geometries. In a particular limit, where the geometry reduces to the recently discovered customizable ${\rm AdS}_2 \times S^2$ of Einstein-Maxwell-dilaton gravity, we compute the static s-wave linearized solutions and characterize the anabasis relating the horizon perturbations to their nonlinear completions within our generalized family of spacetimes.