Yes, Albert Einstein's general theory of relativity played a crucial role in demonstrating that the universe is not static but rather dynamic and evolving. Prior to Einstein's theory, the prevailing view was that the universe was static and unchanging.
Einstein's field equations, formulated in 1915 as part of his general theory of relativity, relate the distribution of matter and energy in the universe to the curvature of spacetime. He discovered that the equations allowed for solutions that described an expanding or contracting universe, in contrast to the static universe assumed at the time.
In 1922, Alexander Friedmann, a Russian mathematician, found solutions to Einstein's equations that described an expanding universe. His work, combined with observations by Edwin Hubble in the late 1920s, provided strong evidence that the universe was indeed expanding. Hubble's observations showed that galaxies were moving away from us, and the farther away they were, the faster they were receding.
Einstein initially resisted the idea of an expanding universe and introduced a cosmological constant into his equations to maintain a static universe. However, in 1929, Hubble's observations became widely accepted, and Einstein acknowledged his mistake, describing the introduction of the cosmological constant as his "greatest blunder."
The realization that the universe was expanding had significant implications. If the universe was expanding, it meant that it had a beginning—an event now known as the Big Bang. This marked a paradigm shift in our understanding of the cosmos, from a static and eternal universe to a dynamic and evolving one.
So, while Einstein did not directly prove that the universe was not static, his theory of general relativity provided the mathematical framework and allowed for solutions that described an expanding universe. Observations by Hubble and subsequent cosmological research have since provided strong empirical evidence supporting the expanding nature of the universe.