Papapetrou field as the gravitoelectromagnetic field tensor in stationary spacetimes

TL;DR

This paper reformulates the vacuum Einstein equations in stationary spacetimes using the Papapetrou field as a gravitoelectromagnetic tensor, providing a differential forms approach and applying junction conditions to specific solutions.

Contribution

It introduces a novel formalism expressing Einstein equations in terms of gravitoelectromagnetic fields using differential forms, and applies it to junction conditions in stationary spacetimes.

Findings

Reformulation of Einstein equations in gravitoelectromagnetic terms

Derivation of junction conditions using this formalism

Application to Van Stockum solutions

Abstract

Introducing the well known Papapetrou field as the gravitoelectromagnetic field tensor, we express the Maxwell-type part of the 3-dimensional quasi-Maxwell form of the {\it vacuum} Einstein field equations in terms of differential forms, analogous to their electromagnetic counterparts in curved spacetimes. Using the same formalism we introduce the junction conditions on non-null hypersurfaces in terms of the introduced gravitoelectromagnetic 4-vector fields and apply them to the case of the Van Stockum interior and exterior solutions.