ABSTRACT

We now have at our disposal all the mathematical tools that are needed to understand the general theory of relativity and the account it oers of gravitational phenomena. Chapter 2 ended with the question `what is the structure of our spacetime?' A priori, the possibilities are limitless: for a start, there are innitely many dimensionalities to choose from. However, because special relativity accounts extremely well for a great many phenomena, it is clear that our spacetime must be quite similar to Minkowski spacetime. Our rst task in this chapter will be to use this observation to restrict the range of possibilities that need to be considered in practice, which is more or less equivalent to adopting the principle of equivalence mentioned in Chapter 2. The next step will be to nd out how a given geometrical structure aects the behaviour of material objects, and this will show us how deviations of this structure from that of Minkowski spacetime can be interpreted in terms of gravitational forces. Finally, we shall investigate how the geometrical structure is determined|or at any rate in uenced|by the distribution of gravitating matter and take a look at some of the phenomena that are predicted by our new theory.