Hidden symmetries in 5D supergravities and black rings

TL;DR

This paper develops a new algebraic method using hidden symmetries in 5D supergravities to generate and analyze charged black ring solutions, simplifying the solution construction process.

Contribution

It introduces a matrix-based generating technique leveraging hidden symmetries for constructing black ring solutions in 5D supergravities.

Findings

Constructed a matrix representation for symmetry transformations.

Provided a method to generate general charged black rings.

Simplified solution derivation via matrix-valued dualisation.

Abstract

We construct generating technique for 5D minimal and $U(1)^3$ supergravities based on hidden symmetries arising in dimensional reduction to three dimensions. In the three-vector case the symmetry is SO(4,4), and the minimal case corresponds to contraction of this group to $G_{2(2)}$. The matrix representation is presented applicable to both cases and the generating transformations preserving an asymptotic structure are listed. Our transformations contain enough free parameters to construct the general charged black ring in $U(1)^3$ theory starting with known solutions. To avoid a complicated inverse dualisation in the component form we introduce the matrix-valued dualisation which opens the way to derive new solutions purely algebraically from the coset representation of the seed.