Correções em Relatividade Geral advindas de modelos com violação espontânea da simetria de Lorentz por um campo bumblebee.

Abstract

The gravitational sector of Standard Model Extension (SME) is studied, and the effects of Lorentz violating terms in physical quantities that test the General Relativity (GR) are explored. We analyze a specific model where the violation occurs spontaneously, through the dynamics of a single vector called bumblebee field. We initiate this work by making a general discussion about Lorentz transformations and Lorentz group, the basic elements that allow us to speak in Lorentz symmetry. We distinguish between observer and particle transformations, equivalent concepts in Special Relativity (SR) but with an important distinction in Lorentz violating models. After, we present a well known model of Classical Field Theory to illustrate how the symmetry is spontaneously broken at a classical context. We present the lagrangian of MPE and we discuss in details its gravitational sector. A general discussion of bumblebee models is made, and then we present the theoretical model we work. After we restrict our analysis to minimum energy of bumblebee field, we calculate some physical quantities of interest. The field equations of model are obtained and a vacuum solution of a spherically symmetric spacetime is encountered (modified Schwarzschild metric). We make a brief discussion about the physical reality of the modification encountered, with the aim to show it is not a fake modification that could be eliminated by a coordinate transformation. With the found metric, we calculate some known physical quantities that test the GR. We finalize this work by imposing a superior limit on the violating parameters for each test made.