Introdução à relatividade e à métrica de Schwarzschild

Abstract

This paper presents a theoretical study of the foundations of restricted relativity, focusing on the geometric description of space-time, as well as the physical implications of the Schwarzschild metric. Initially, the concepts of intervals, Lorentz transformations and relativistic effects are developed, presenting real experiments that prove effects such as time dilation and space contraction. Next, the Schwarzschild metric is presented, considering it to describe time dilation in a stationary rocket around a black hole, demonstrating the relationship between proper time and coordinated time according to the distance to the event horizon, also using real data to calculate the correction required for GPS operation. Finally, concepts of relativistic dynamics are discussed, demonstrating that the relativistic expression of energy recovers Newton’s classical kinetic energy in the limit of low speeds. The results show the internal consistency of the theory of relativity and its ability to generalize classical mechanics in regimes of high gravity or speed.