Nature of the vorticity in the G\"{o}del spacetime

TL;DR

This paper investigates the nature of vorticity in G"odel spacetime, revealing it differs from typical stationary spacetimes and may explain gyroscope anomalies, by analyzing vorticity definitions and superenergy flow.

Contribution

It introduces two definitions of vorticity to distinguish cases with and without superenergy circular flow in G"odel spacetime.

Findings

Vorticity in G"odel spacetime is not linked to circular superenergy flow.

Different vorticity definitions help differentiate spacetime behaviors.

Supports explanation for gyroscope anomalies in G"odel spacetime.

Abstract

The physical meaning of the vorticity of the matter content in G\"{o}del spacetime is analyzed in some detail. As we shall see, unlike the situation in general stationnary axially symmetric spacetimes (Lewis--Papapetrou), the vorticity in G\"{o}del spacetime is not associated to a circular flow of superenergy on the plane orthogonal to the vorticity vector. This fact might be at the origin of the strange behaviour of gyroscopes in such spacetime. The analysis emerging from the tilted version of G\"{o}del spacetime supports further this point of view. In order to tell apart the two situations (with and without circular flow of superenergy) we introduce two different definitions of vorticity, related to the presence (absence) of such a flow.