Nonperturbative gravito-magnetic fields

TL;DR

This paper investigates the behavior of gravito-magnetic fields in nonlinear gravity, showing that the transverse condition valid in linear theory generally does not hold in realistic, inhomogeneous models, except under special symmetries.

Contribution

It demonstrates that nonlinear gravito-magnetic fields cannot maintain transversality in generic inhomogeneous models, highlighting the importance of symmetries for such conditions.

Findings

Transverse condition fails in nonlinear regimes for realistic models.

Special symmetries like Bianchi and G2 can preserve transversality.

Nonlinear gravito-magnetic fields are necessarily non-transverse in general.

Abstract

In a cold matter universe, the linearized gravito-magnetic tensor field satisfies a transverse condition (vanishing divergence) when it is purely radiative. We show that in the nonlinear theory, it is no longer possible to maintain the transverse condition, since it leads to a non-terminating chain of integrability conditions. These conditions are highly restrictive, and are likely to hold only in models with special symmetries, such as the known Bianchi and $G_2$ examples. In models with realistic inhomogeneity, the gravito-magnetic field is necessarily non-transverse at second and higher order.