Aplicações de geometria de Riemann no estudo de movimento geodésico no espaço-tempo de Schwarzschild

Abstract

In this work, we present a detailed discussion of the relation between four and threedimensional quantities used in the description of geodesic motion in General Relativity. We apply the resulting formalism to study radial motion in Schwarzschild space-time, and correct some results known in the literature. In particular, we show that "repulsion" in the Schwarzschild field can not accelerate an outgoing particle, and thus represents pure coordinate effect. In other words, the repulsion can not be detected neither by local nor by distant observer. Results of this work were recently published in Astroparticle Physics, 2019, vol. 107, p. 35-37.