Extended gravitoelectromagnetism. I. Variational formulation
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: 27 March 2021
Published online: 8 April 2021
This work presents a novel approach to well established concepts of gravity, formulating a new and consistent gravitoelectromagnetic theory. The long standing gravitoelectromagnetic field theory is considered in the framework of Hamilton’s principle. A variational formulation based on this principle describes the dynamics of a fully-relativistic perfect fluid in the presence of the gravitoelectromagnetic field in flat space, leading to the definition of the fluid and field energy-momentum tensors. A relativistic Cauchy invariant for a compressible fluid immersed in the gravitoelectromagnetic field is demonstrated. The gravitoelectromagnetic fluid equations of motion are written in covariant form suited for calculating higher-order relativistic effects. The integral form of the conservation theorems is presented, as well as equations that describe the excitation of gravitoelectromagnetic waves. As an application, the equations of motion are used to derive the equation that governs the galactic rotation according to gravitoelectromagnetism.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021