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Abstract

Einstein's theory of general relativity is empirically verified to be the most successful model of gravitational phenomena. Its theoretical structure is both elegant and simple. On the other hand, in its strong-field limit, the theory has two major flaws. First, it is isolated'from the mainstream of physical laws and in particular, it is not amen-abl© to quantization. Second, by being essentially a singular theory it paradoxially predicts the inevitable gravitational collapse with its attendant formation of "black holes" the evidence for the existence of which is rather weak.

This setback of Einstein's model has motivated us to search for an alternative that will be both nonsingular and more amenable to quanti-zation or at least possesses one of these features. In this thesis we explore the possibility of developing such an alternative using a variational approach based on a Lagrangian which is a nonlinear function of the scalar curvature.

We start with a general review and critique of the existing situation which puts our own contribution in its proper perspective. This contribution commences with a new derivation of the field equations which leads to a necessary condition on the structure of the Lagrangians.

By concentrating on static, isotropic free-field metrics, we obtain coupled ordinary differential equations for the metric coefficients and the scalar curvature in terms of the Lagrangian and its derivatives. This enables us to fix the asymptotic properties of the corresponding specetimes and hence to single out and classify viable Lagrangians.

Several examples are developed including the quadratic and more general Lagrangians. By appealing to the classical limit of an under-lying quantum theory (i.e. the finiteness, and smallness of Planck's constant) we find solution spacetimes which have good behaviour in both strong- and weak-field limits.

We then extend the quantum connection to consider solutions which become complex-valued in the strong-field domain and obtain an interesting result.

The thesis ends with a resume and general outlook.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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