Sigma-model approaches to exact solutions in higher-dimensional gravity and supergravity

TL;DR

This paper explores sigma-model methods for generating exact solutions in higher-dimensional gravity and supergravity, focusing on symmetry groups and solution construction techniques, including black ring solutions.

Contribution

It introduces the sigma-model approach to higher-dimensional gravity and supergravity, detailing the use of invariance groups for solution generation and recent advances in black ring solutions.

Findings

Application of sigma-model techniques to 5D gravity and supergravity.

Identification of invariance groups SL(3,R) and G_{2(2)}.

Progress in constructing charged rotating black rings.

Abstract

Classical gravitating field theories reduced to three dimensions admit manifest gauge invariances and hidden symmetries, which together make up the invariance group G of the theory. If this group is large enough, the target space is a symmetric space G/H. New solutions may be generated by the action of invariance transformations on a seed solution. Another application is the construction of multicenter solutions from null geodesics of the target space. After a general introduction on this sigma-model approach, I will discuss the case of five-dimensional gravity, with invariace group SL(3,R), and minimal five-dimensional supergravity, with invariance group G_{2(2)}. I will also describe recent attempts at the generation of new charged rotating black rings.