Deciphering and generalizing Demianski-Janis-Newman algorithm

TL;DR

This paper clarifies and extends the Demiański-Janis-Newman algorithm, enabling systematic generation of new solutions in supergravity by explaining complexification procedures and generalizing to various horizon topologies and charges.

Contribution

It explains the hidden assumptions, generalizes the algorithm to topological horizons and charged solutions, and introduces a new hyperbolic horizon solution.

Findings

Provided a systematic method for complexification of metric functions.

Extended Demiański metric to hyperbolic horizons.

Facilitated applications in supergravity and related theories.

Abstract

In the case of vanishing cosmological constant, Demia\'nski has shown that the Janis-Newman algorithm can be generalized in order to include a NUT charge and another parameter $c$, in addition to the angular momentum. Moreover it was proved that only a NUT charge can be added for non-vanishing cosmological constant. However despite the fact that the form of the coordinate transformations was obtained, it was not explained how to perform the complexification on the metric function, and the procedure does not follow directly from the usual Janis-Newman rules. The goal of our paper is threefold: explain the hidden assumptions of Demia\'nski's analysis, generalize the computations to topological horizons (spherical and hyperbolic) and to charged solutions, and explain how to perform the complexification of the function. In particular we present a new solution which is an extension of the Demia\'nski metric to hyperbolic horizons. These different results open the door to applications in (gauged) supergravity since they allow for a systematic application of the Demia\'nski-Janis-Newman algorithm.