Extended gravitoelectromagnetism. II. Metric perturbation
National Institute for Space Research, 12227-010, São José dos Campos, SP, Brazil
2 National Commission for Nuclear Energy, 22294-900, Rio de Janeiro, RJ, Brazil
Accepted: 16 April 2021
Published online: 28 April 2021
This article makes the connection between the new gravitoelectromagnetic theory presented in the part I paper and general gravity in its weak formulation. The perturbation in the metric tensor is obtained in terms of the flat-space total energy–momentum tensor given by the sum of the consistent fully relativistic fluid and gravitoelectromagnetic field contributions. Expressions for the perturbed metric in the internal (fluid) and external (vacuum) regions are given in terms of the fluid and field variables. This formulation of gravitoelectromagnetism is compatible with the formation of gravitational waves. The geodesic equation is obtained in both the internal and external regions, including new terms neglected in the standard gravitomagnetic formulation. It is shown that the new terms reproduce the anomalous shift of planetary precession, which results from a balance between the gravitoelectric and gravitomagnetic forces.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021