Spacetime, Curvature and Gravity

The end result of Einstein’s revolutionary vision is that gravity is simply the manifestation of the curvature of spacetime. This is a concept that has a deep significance and is at the heart of the Einstein field equations. This Chapter will explain why we need to introduce the idea of 'spacetime' and how we can define the concept of spacetime curvature in this description. Starting from the example of a spacetime empty of matter – that is, a flat spacetime – we will move to the example of a spacetime containing matter and energy – that is, a curved spacetime. This chapter will explain why we find the description of gravity proposed by Newton very reasonable and why we have trouble appreciating the new vision proposed by Einstein. We will contrast the two descriptions with a simple example and show how the very same physical phenomenon – the orbit of the Earth around the Sun – can be seen with very different explanations by Newton and Einstein.