Time and spacetime in general relativity (Gr)

Abstract

This chapter begins consideration of foundations for general relativity. This is both a relativistic theory of gravitation and a freeing from absolute or background structures (as Chaps. 8 to 10 explain further). The latter perspective emphasizes Background Independence, a notion widely used in Quantum Gravity programs as well. Given the substantial conceptual and technical differences incurred by Background Independence, we further motivate the first—and only observationally established—seat of this—general relativity—by firstly briefly surveying observational evidence for general relativity. Secondly, by outlining useful features of some of its simpler cosmological and black hole solutions. We then continue to discuss our preamble’s focal topics—the nature of time, space, spacetime, frames, clocks and ‘rods’—now in the context of general relativity. This chapter works in the spacetime setting (as opposed to the next chapter’s dynamical setting). On the one hand, special and general relativistic spacetimes enjoy some parallels such as similar types of notions of causality and simultaneity. On the other hand, general relativity’s Background Independence produces many difference between general relativity’s rendition of the focal topics and both Newtonian theory’s and special relativity’s. This occurs in particular through general relativity being diffeomorphism invariant, which corresponds to a far larger and more nuanced invariance group than the Lorentz and Poincaré groups of special relativity. In anticipation to Chap. 11 ’s introduction to Quantum Gravity, we end by outlining how general relativity points to its own limitation in the form of singularity theorems.