Nutty Kaluza-Klein dyons revisited

TL;DR

This paper explores extended solutions in Kaluza-Klein theory with independent dilaton charge, revealing new singular solutions, analyzing their properties, and showing the absence of closed timelike geodesics in Nutty KK dyons.

Contribution

It introduces a generalized charge matrix approach, uncovers new singular solutions, and investigates the geodesic and wormhole properties of Nutty KK dyons.

Findings

Identified three branches of dilaton charge, including new singular solutions.

Demonstrated dilaton charge prevents wormhole formation from super-extreme solutions.

Showed no closed timelike geodesics exist around Nutty KK dyons.

Abstract

We extend the previous analysis of (locally) asymptotically flat solutions of Kaluza-Klein (KK) theory by assuming that the dilaton charge is an independent parameter. This corresponds to a general nondegenerate matrix of charges within the geodesic sigma model approach and comes into contact with singular solutions of the four-dimensional Einstein-scalar theory. New features of the degenerate class of solutions, which includes regular KK black holes, are also revealed. Solving the constraint equation, we find three distinct branches of the dilaton charge as a function of the other asymptotic charges, one of which contains the previously known solutions, and the other two, related by electric/magnetic duality, are new and singular. We also investigate whether a super-extreme non-rotating solution in the presence of a Newman-Unti-Tamburino (NUT) charge can become a wormhole, as is the case in Einstein-Maxwell theory. It is shown that the dilaton prevents this possibility, while non-traversable five-dimensional vacuum gravitational wormholes can exist. Finally, we analyze the geodesic structure within the chronosphere around the Misner string of Nutty KK dyons, showing that there are no closed timelike geodesics.