Two scientists more than anyone else have contributed in defining our understanding of gravity: Newton in 1679 and Einstein in 1915. The mathematical frameworks the two have developed and proposed, however, are very different. Newton’s gravity is the one we learn at school and is normally taught at university. It provides a very natural interpretation of what we experience - the apple falls from the tree because the Earth attracts it! Einstein’s gravity is studied only in the most advanced courses at the university and provides a very counterintuitive explanation, requiring the concepts of spacetime and curvature. This chapter will provide a first description of the Einstein equations and, although it will not enter into the mathematical aspects of the equations, it will explain the basic concepts behind them. Acquiring a first qualitative understanding of Einstein equations will be useful to comprehend better the concept of spacetime curvature discussed in Chapter 4.

Famously, Klein and Einstein were embroiled in an epistolary dispute over whether General Relativity has any physically meaningful conserved quantities. This chapter explores the consequences of Noether’s second theorem for this debate and connects it to Einstein’s search for a ‘substantive’ version of general covariance as well as his quest to extend the Principle of Relativity. The chapter’s argument is that Noether’s second theorem provides a clear way to distinguish between theories in which gauge or diffeomorphism symmetry is doing real work in defining charges, as opposed to cases in which this symmetry stems from Kretchmannization. Finally, a comment is made on the relationship between this Noetherian form of substantive general covariance and the notion of ‘background independence’.