Problemas fundamentais da gravitação sob o prisma tensorial.

Abstract

In this work we present the tensor formalism of gravitation in conceptual, analytical and, when necessary, numerical aspects. Initially, we offer a kind of tutorial about the tensor calculus and historical aspects of Einstein’s theory of relativity, to present to the reader a more real view of the subject of our research. In the following, we opened way to operate the main tensor of general relativity, the Einstein tensor. We show that this object holds one of the most significant results of this theory. We work such object to reproduce the famed Schwarzschild solution. Moreover, knowing that Einstein’s gravitation is a theory with experimental support, we consider crucial to remember that the theory is compatible with the precession of the perihelion of Mercury. This result, in addition to validating the theory in question, gives an opportunity to approach about symmetries of space-time. We show that some symmetries are closely linked to the Killing tensors. We can anticipate that such objects reveal hidden symmetries in space-time and are surrounded by peculiarities, many of which are disclosed in this work.