Charged black rings from inverse scattering

TL;DR

This paper reviews the inverse scattering method for constructing black hole solutions in higher-dimensional gravity theories and demonstrates its application by explicitly constructing a charged black ring in Einstein-Maxwell-dilaton theory.

Contribution

It provides a detailed review of the inverse scattering method and applies it to construct the first electrically charged black ring in Einstein-Maxwell-dilaton theory.

Findings

Successful construction of a charged black ring solution.

Demonstrates the effectiveness of inverse scattering in EMd theory.

Extends known black hole solutions to include electric charge.

Abstract

The inverse scattering method of Belinsky and Zakharov is a powerful method to construct solutions of vacuum Einstein equations. In particular, in five dimensions this method has been successfully applied to construct a large variety of black hole solutions. Recent applications of this method to Einstein-Maxwell-dilaton (EMd) theory, for the special case of Kaluza-Klein dilaton coupling, has led to the construction of the most general black ring in this theory. In this contribution, we review the inverse scattering method and its application to the EMd theory. We illustrate the efficiency of these methods with a detailed construction of an electrically charged black ring.