New approach to solution generation using SL(2,R)-duality of a dimensionally reduced space in five-dimensional minimal supergravity and new black holes

TL;DR

This paper introduces a new solution generation method in five-dimensional minimal supergravity using SL(2,R)-duality, leading to novel rotating Kaluza-Klein black hole solutions with six charges.

Contribution

It develops a formalism leveraging SL(2,R)-duality in reduced supergravity to generate new black hole solutions from known ones.

Findings

Generated rotating Kaluza-Klein black holes with six charges.

Demonstrated the formalism on Rasheed solutions.

Identified charge relations among the solutions.

Abstract

The dimensional reduction of (the bosonic sector of) five-dimensional minimal supergravity to four dimensions leads to a theory with a massless axion and a dilaton coupled to gravity and two U(1) gauge fields (one of which has Chern-Simons coupling), whose field equations have SL(2,R)-invariance. Utilizing this SL(2,R)-duality, we provide a new formalism for solution generation. As an example, applying it to the Rasheed solution, which are known to describe dyonic rotating black holes (from the four-dimensional point of view) of five-dimensional pure gravity, we obtain rotating Kaluza-Klein black hole solutions in five-dimensional minimal supergravity. We also show that the solutions have six charges: mass, angular momentum, Kaluza-Klein electric/magnetic charges and electric/magnetic charges of the Maxwell field, four of which are related by a constraint.