Relatividade geral, buracos negros e ondas gravitacionais

Abstract

In this study, firstly, the basic ideas, concepts and principles of Special Relativity are introduced, to help understand the construction of General Relativity. The second chapter is an introduction to the mathematical formalism of General Relativity, such as the covariant derivative, Riemann tensor and parallel transport. In the next chapter the construction of Einstein's equation using a classical approach is shown. The last two chapters present the first two solutions of Einstein's equation, the first is the Schwarzschild solution, which contains the precession of Mercury's perihelion and the surprising result: the existence of black holes. The last one is a solution given by Einstein, which consists of linearizing his equation using a small disturbance in the metric. This solution shows the existence of gravitational waves in the space-time, how they are produced, how they propagate and how to detect them.