"Flip" of SL(2,R)-duality in five-dimensional supergravity

TL;DR

This paper explores duality transformations in five-dimensional supergravity when reduced to four dimensions with different Killing vector choices, leading to new solution-generation methods and rotating black hole solutions with NUT parameters.

Contribution

It introduces a novel duality transformation technique for timelike reductions and applies it to generate new rotating Kaluza-Klein black hole solutions.

Findings

Developed a new duality transformation for timelike reductions.

Generated rotating Kaluza-Klein black hole solutions with NUT parameters.

Identified conditions under which solutions are asymptotically flat.

Abstract

The dimensional reduction of the bosonic sector of five-dimensional minimal supergravity to a Lorentzian four-dimensional spacetime leads to a theory with a massless axion and a dilaton coupled to gravity and two U(1) gauge fields and the dimensionally reduced equations of motion have SL(2,R)/SO(2)-duality invariance. In our previous work, utilizing the duality invariance, we formulated solution-generation techniques within five-dimensional minimal supergravity. In this work, by choosing a timelike Killing vector, we consider dimensional reduction to a four-dimensional Euclidean space, in which the field equations have SL(2,R)/SO(1,1) invariance. In the timelike case, we develop a new duality transformation technique, while in the spacelike case we have done that in the previous work. As an example, by applying it to the Rasheed solutions, we obtain rotating Kaluza-Klein black hole solutions in five-dimensional minimal supergravity. In general, in contrast to the spacelike case, the resulting dimensionally reduced solution includes the so-called NUT parameter and therefore from a four-dimensional point of view, such a spacetime is not asymptotically flat. However, it is shown that in some special cases, it can describe ordinary Kaluza-Klein black holes.