Geometry and Physics without Gravity: Special Relativity

Abstract

The next two chapters deal with Einsteins theory of relativity, which will be needed to discuss gravitational waves and collapse in Chapter 8 and relativistic mechanics in Chapter 9. This is, by no means, a book on relativity, so we will try to keep the treatment and mathematics of relativity as simple as possible and yet still construct all the concepts and tools that are needed to tinker with black hole engines.1 Knowledge of relativity requires a knowledge of geometry and considerably more than high school or college geometry. Nevertheless, that is where we will start, and then develop only enough to understand metrics and four dimensional spacetime (which is crucial to even begin understanding black holes).We then shall introduce the basic concepts of mechanics like time dilation, Lorentz transformations, four vectors, and relativistic beaming. And, finally, we will begin our extended discussion on fluid dynamics and electromagnetism, but deal here with flat spacetime only. Once we have covered Einsteins theory of gravity in Chapter 7, will we return to this subject and go into more depth in Chapter 9.