Spacetime Geometry of Relativity: Extending Pythagorean Theorem

The theory of relativity was created by Einstein in two stages, extending over a decade from 1905 to 1915. General relativity is said to be the most powerful tool that can be used to explain the behavior of the universe.In this book, we try to comprehend the universe with a fundamental formula known as the Pythagorean theorem, used as a vehicle to review the essence of Euclidean geometry and non-Euclidean geometry, then move on to Newtonian mechanics, and review the historical development of electromagnetism, setting the stage for special relativity. Next, we describe Einstein’s efforts to generalize his theory to include gravitation, which led to a geometric theory of spacetime: the gravitational field equations. The German astronomer Schwarzschild quickly solved these equations for a special case. Also presented are the numerical graphical results of the planetary orbits and light trajectories using the Python code that we created. Then the reader is taken on an excursion to the physics of the microcosm, describing how special relativity was instrumental in the development of quantum theory, and how several Japanese physicists contributed to atomic and particle physics. Finally, we end the book by introducing the work of Roger Penrose on black holes, which is closely related to Schwarzschild’s solution, and the existence of intrinsic singularity at the center of black holes. In his intriguing theory of Conformal Cyclic Cosmology, our universe may be one in a never-ending birth-and-death cycle of universes.