Banca de QUALIFICAÇÃO: ELVES SILVA MOREIRA

CONGRUENCES IN GENERAL RELATIVITY AND COSMOLOGICAL CONSEQUENCES

Time-like congruences, kinematic parameters, evolution equations, Raychaudhuri equation, FRW models.

Einstein's General Theory of Relativity (GRT) is characterized as a geometric theory of gravitation, since its formulation deals with an identification between the geometry of four-dimensional space-time (1 temporal dimension plus 3 spatial dimensions) and the total content of matter. - existing energy. Every theory of gravitation suggests a corresponding cosmology. Thus, just as Newton's Theory of Gravitation supported the development of a Newtonian Cosmology, the TRG enabled the formulation of Relativistic Cosmological Models. The first relativistic model of the Universe was obtained by Einstein himself, in 1917. The second relativistic model of the Cosmos was formulated by Friedmann, between 1922 and 1924. In this work, the so-called Friedmann Metrics are reproduced through congruences of the time-type. Friedmann's cosmological models constitute the theoretical starting point for the elaboration of the Standard Cosmological Model (SPM), also called the -CDM model. Although historically outdated, the detailed study of the first cosmological models constitutes a rich mathematical laboratory to acquire maturity for future studies and research in Gravitation and Cosmology.