Gravoelectric-dual of the Kerr solution

TL;DR

This paper introduces a gravoelectric duality transformation based on curvature decomposition, deriving a dual Kerr solution interpreted as a Kerr black hole in a string dust universe, highlighting duality invariance in vacuum equations.

Contribution

It defines a new gravoelectric duality transformation and derives the dual Kerr solution, expanding understanding of dualities in gravitational solutions.

Findings

Duality-invariant vacuum equations identified.

Dual Kerr solution obtained and interpreted.

Kerr black hole in a string dust universe modeled.

Abstract

By decomposing the Riemann curvature into electric and magnetic parts, we define the gravoelectric duality transformation by interchange of active and passive electric parts which amounts to interchange of the Ricci and Einstein tensors. It turns out that the vacuum equation is duality-invariant. We obtain solutions dual to the Kerr solution by writing an effective vacuum equation in such a way that it still admits the Kerr solution but is not duality invariant. The dual equation is then solved to obtain the dual-Kerr solution which can be interpreted as the Kerr black hole sitting in a string dust universe.