Relative-observer definition of the Simon tensor

TL;DR

This paper generalizes the Simon tensor's definition from Kerr spacetime to any spacetime and observer family using a 3+1 splitting of Bianchi identities, broadening its applicability.

Contribution

It introduces a new observer-dependent formulation of the Simon tensor applicable to general spacetimes through a 3+1 decomposition.

Findings

Provides a generalized, observer-dependent Simon tensor definition.

Rewrites Bianchi identities as a balance equation for spatial fields.

Extends the concept beyond Kerr spacetime to arbitrary spacetimes.

Abstract

The definition of Simon tensor, originally given only in the Kerr spacetime and associated with the static family of observers, is generalized to any spacetime and to any possible observer family. Such generalization is obtained by a standard "3+1" splitting of the Bianchi identities, which are rewritten here as a "balance equation" between various spatial fields, associated with the kinematical properties of the observer congruence and representing the spacetime curvature.