Nonlinear hidden symmetries in General Relativity and String Theory: a matrix generalization of the Ernst potentials

TL;DR

This paper discusses a matrix generalization of Ernst potentials in General Relativity and String Theory, enabling the generation of new exact solutions with hidden symmetries, including complex black hole configurations.

Contribution

It introduces a matrix formalism extending Ernst potentials to higher-dimensional theories, facilitating the discovery of new solutions in string theory and gravity.

Findings

Matrix Ernst potentials enable solution generation in higher dimensions.

Hidden symmetries allow constructing charged black objects.

Formalism applicable to theories with D≥5 dimensions.

Abstract

In this paper we recall a simple formulation of the stationary electrovacuum theory in terms of the famous complex Ernst potentials, a pair of functions which allows one to generate new exact solutions from known ones by means of the so-called nonlinear hidden symmetries of Lie-Backlund type. This formalism turned out to be very useful to perform a complete classification of all 4D solutions which present two spacetime symmetries or possess two Killing vectors. Curiously enough, the Ernst formalism can be extended and applied to stationary General Relativity as well as the effective heterotic string theory reduced down to three spatial dimensions by means of a (real) matrix generalization of the Ernst potentials. Thus, in this theory one can also make use of nonlinear matrix hidden symmetries in order to generate new exact solutions from seed ones. Due to the explicit independence of the matrix Ernst potential formalism of the original theory (prior to dimensional reduction) on the dimension D, in the case when the theory initially has D>=5, one can generate new solutions like charged black holes, black rings and black Saturns, among others, starting from uncharged field configurations.