@Article{RochaMarMalCarLud:2021:BeGrAp,
               author = "Rocha, Fl{\'a}via and Marinho J{\'u}nior, Rubens and Malheiro, 
                         Manuel and Carvalho, Geanderson Ara{\'u}jo and Ludwig, Gerson 
                         Otto",
          affiliation = "{Instituto Tecnol{\'o}gico de Aeron{\'a}utica (ITA)} and 
                         {Instituto Tecnol{\'o}gico de Aeron{\'a}utica (ITA)} and 
                         {Instituto Tecnol{\'o}gico de Aeron{\'a}utica (ITA)} and 
                         {Universidade do Vale do Para{\'{\i}}ba (UNIVAP)} and {Instituto 
                         Nacional de Pesquisas Espaciais (INPE)}",
                title = "Beyond gravitomagnetism with applications to Mercury's perihelion 
                         advance and the bending of light",
              journal = "International Journal of Modern Physics D",
                 year = "2021",
               volume = "30",
               number = "10",
                pages = "e2150073",
                month = "July",
             keywords = "beyond gravitomagnetism, General relativity, gravitomagnetism, 
                         perturbation theory.",
             abstract = "The expansion of both sides of Einstein's field equations in the 
                         weak-field approximation, up to terms of order 1/c4 is derived. 
                         This new approach leads to an extended form of gravitomagnetism 
                         (GEM) properly named as Beyond Gravitomagnetism (BGEM). The metric 
                         of BGEM includes a quadratic term in the gravitoelectric potential 
                         n the time and also space metric functions in contrast with first 
                         post-Newtonian 1PN approximation where the quadratic term appears 
                         only in the time metric function. This nonlinear term does not 
                         appear in conventional GEM, but is essential in achieving the 
                         exact value of Mercury's perihelion advance as we explicitly show. 
                         The new BGEM metric is also applied to the classical problem of 
                         light deflection by the Sun, but the contribution of the new 
                         nonlinear terms produce higher-order terms in this problem and can 
                         be neglected, giving the correct result obtained already in the 
                         Lense-Thirring (GEM) approximation. The BGEM approximation also 
                         provides new terms that depend on the dynamics of the system, 
                         which may bring new insights into galactic and stellar physics.",
                  doi = "10.1142/S0218271821500735",
                  url = "http://dx.doi.org/10.1142/S0218271821500735",
                 issn = "0218-2718",
             language = "en",
           targetfile = "Rocha_beyond.pdf",
        urlaccessdate = "12 maio 2024"
}