Ondas gravitacionais: um estudo comparativo sob as perspectivas newtoniana e relativística

Abstract

This work aims to explore the concept of gravitational waves through a comparative approach between Newtonian and relativistic perspectives. Initially, an introduction to the phenomenon of gravitational waves is presented, its relevance in the context of modern astrophysics and its experimental detection, with emphasis on observatories such as LIGO and Virgo. In the Newtonian approach, a simplified description is considered based on two point bodies in circular motion emitting gravitational radiation. In this scenario, we found the necessary equations to quantitatively understand the experimental results pointed out in the article on the discovery of gravitational waves by the LIGO collaboration. Although limited, this perspective is useful for introducing basic concepts and developing intuition about system behavior. Next, we enter relativistic formalism, using Einstein’s theory of General Relativity. In this regime the spacetime metric is perturbed around a flat solution (Minkowski metric), and Einstein’s equations are linearized to derive the equations that govern the propagation of gravitational waves in spacetime. At the end, we will analyze the proximity between the two regimes and comment on the influences of our approaches, emphasizing the main limits of classical theory and its need for didactic purposes that facilitate the introduction to the topic.