Basics of General Relativity

Abstract

General relativity (hereafter GR) is the subject dealing with the structure of space-time and with how to describe physical laws in any given space-time. The perspective of space-time in GR is very different from that in Newtonian physics. In Newtonian physics, space is considered to be flat, infinite and eternal, time is considered to flow uniformly, and physical processes are considered to act in this external space-time frame. In the framework of GR, however, space-time is a four-dimensional manifold which may be curved and the properties of space-time itself are determined by dynamical processes. This appendix provides a brief summary of the aspects of GR that are used in this book. More details can be found in the excellent textbooks by Weinberg (1972), Misner et al. (1973), Rindler (1977), and Carroll (2004). Space-time Geometry In order to gain some insight in how to describe space-time as a four-dimensional manifold (hypersurface), consider a two-dimensional analog. To describe a two-dimensional surface, we can construct a coordinate system and label each point on the surface by its coordinates. The geometrical properties of the surface can be obtained by considering the distance between each pair of infinitesimally close points on the surface in terms of the differences in coordinates.