FlippedSL(2,R)duality in five-dimensional supergravity

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 Uð1Þ gauge fields and the dimensionally reduced equations of motion have SLð2; RÞ=SOð2Þ-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 SLð2; RÞ=SOð1; 1Þ 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 (Newman, Unti, and Tamburino) 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.

General Kaluza-Klein black holes with all six independent charges in five-dimensional minimal supergravity

“…As shown in the list, the most general black hole solutions with full six independent charges, which are expected to exist [11], have not been discovered so far. The aim of this paper is to present such exact solutions describing general Kaluza-Klein black holes with full six charges obtained by using our framework [10,12] of the SL(2, R)-duality.…”

Kaluza-Klein black lens in five dimensions

“…In particular, physics of black holes in five-dimensional Einstein-Maxwell-Chern-Simons (EMCS) theory has recently been the subject of increased attention, since the five-dimensional EMCS theory describes the bosonic sector of five-dimensional minimal supergravity as a low-energy limit of string theory, as well as one of the simplest theories of supersymmetry. So far, several types of black hole solutions in this theory have been found by using recent development of solution generating techniques [1][2][3][4][5][6][7][8][9] and they have been classified in the context of the uniqueness theorems [10][11][12]. However, it is evident that the construction of all black hole solutions has not been achieved yet.…”