Generating solutions via sigma-models

TL;DR

This paper reviews recent techniques for generating solutions to Einstein equations in four and five dimensions, focusing on sigma-model methods that facilitate constructing complex black hole and black ring solutions.

Contribution

It introduces a unified sigma-model framework for solution generation in higher-dimensional Einstein theories with various matter fields, enabling new black ring solutions.

Findings

Developed solution-generating techniques using sigma-models.

Applied methods to Einstein-Maxwell-dilaton-axion and supergravity models.

Opened pathways to construct general charged black rings in five dimensions.

Abstract

We review recent development of solution-generating techniques for four and five-dimensional Einstein equations coupled to vector and scalar fields. This includes D=4 Einstein-Maxwell-dilaton-axion theory with multiple vector fields, D=5 Einstein-Maxwell gravity with the Chern-Simons term (minimal five-dimensional supergravity), and some other models which attracted attention in connection with black rings. The method is based on reduction to three-dimensional gravity coupled sigma-models with symmetric target spaces. Our recent results open a way to construct the general charged black rings in five-dimensional supergravity possibly coupled to vector multiplets.