Introduction

The description of gravity based on Einstein's general theory of relativity is quite satisfactory in most respects. It has been repeatedly verified experimentally as regards those features which could be directly tested while other parts of it are conceptually very elegant and beautiful. Nevertheless, it is obvious that this theory is fundamentally flawed or – at the least – incomplete.

Such a conclusion emerges from the fact that there exist well defined situations in which the theory is incapable of predicting the future evolution of the dynamical variables owing to the development of singularities. To see this concretely, consider the example of a collapsing sphere of dust described in Chapter 8. An observer comoving along with the dust particle will find that the trajectory of the dust particle hits a singularity (at which the curvature and density diverge) within finite proper time τ as shown by the observer's clock. In other words, the observer can not ascertain beforehand her future evolution for arbitrarily large values of τ using Einstein's theory of gravity. As another example, consider the standard description of our universe in terms of a Friedmann model discussed in Chapter 10. For reasonable values of the parameters of the model at the present moment – which are determined observationally – the theory is incapable of describing the state of the universe, say, 20 billion years ago for any equation of state for high density matter having positive pressure and energy density.