Nonperturbative gravitomagnetic fields

†Department of Fundamental Physics, University of Barcelona, E-08028 Barcelona, Spain§Institute for Theoretical Physics, FSU Jena, Max-Wien-Platz 1, D-07743 Jena, Germany‡School of Computer Science and Mathematics, Portsmouth University, Portsmouth PO1 2EG, England*Department of Mathematics and Applied Mathematics, University of Cape Town, Cape Town 7701, South Africa††Department of Mathematics, Applied Mathematics and Astronomy, University of South Africa, Pretoria 0001, South Africa(15 April 1999)In a cold matter universe, the linearized gravito-magnetic tensor field satisfies a transverse con-dition (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-terminatingchain of integrability conditions. These conditions are highly restrictive, and are likely to hold onlyin models with special symmetries, such as the known Bianchi and G