Classical GR

This chapter covers the essential aspects of classical general relativity, such as probing spacetime curvature with parallel transport of vectors, the geometrical view of curvature and its description through the Christoffel symbols, and the Einstein field equations. The invariance of the theory under active diffeomorphisms is discussed, motivating the search for a background-independent theory of quantum gravity in later chapters. The geometrical intuition for curvature established in this chapter establishes the basis for exploring gauge fields in the subsequent chapters.