ABSTRACT

This chapter discusses the curved spacetime and the physical mathematics of general relativity. Spacetime is curved near gravitating matter. The chapter describes the rubber sheet analogy for spacetime curved by matter. It introduces geodesics during a discussion of the straight world line of a free body in special relativity. Generally, however, the geodesic world lines of bodies under the action of gravity are curved, and there exists no coordinate transformation that will make them look straight, except in one special case. It is difficult enough to imagine a curved three-dimensional space, let alone a curved four-dimensional spacetime, so it explain the idea of curvature by considering two-dimensional surfaces, with which are all familiar. Geometries are mathematical theories; to test which geometry applies to a given surface, which need physical definitions of the quantities appearing in the theory. The chapter discusses the distance along any line as the number of units on a standard measuring tape coincident with the line.