@Article{Ludwig:2021:VaFo,
               author = "Ludwig, Gerson Otto",
          affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)}",
                title = "Extended gravitoelectromagnetism. I. Variational formulation",
              journal = "European Physical Journal Plus",
                 year = "2021",
               volume = "136",
               number = "4",
                pages = "e373",
                month = "Apr.",
             abstract = "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 Hamiltons 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.",
                  doi = "10.1140/epjp/s13360-021-01367-2",
                  url = "http://dx.doi.org/10.1140/epjp/s13360-021-01367-2",
                 issn = "2190-5444",
             language = "en",
           targetfile = "ludwig_extended.pdf",
        urlaccessdate = "21 maio 2024"
}