A class of perfect fluids in general relativity

This thesis is concerned with exact solutions of Einstein's field equations of general relativity, in particular, when the source of the gravitational field is a perfect fluid with a purely electric Weyl tensor. General relativity, cosmology and computer algebra are discussed briefly. A mathematical introduction to Riemannian geometry and the tetrad formalism is then given. This is followed by a review of some previous results and known solutions concerning purely electric perfect fluids. In addition, some orthonormal and null tetrad equations of the Ricci and Bianchi identities are displayed in a form suitable for investigating these space-times. Conformally flat perfect fluids are characterised by the vanishing of the Weyl tensor and form a sub-class of the purely electric fields in which all solutions are known (Stephani 1967). The number of Killing vectors in these space-times is investigated and results presented for the non-expanding space-times. The existence of stationary fields that may also admit 0, 1 or 3 spacelike Killing vectors is demonstrated. Shear-free fluids in the class under consideration are shown to be either non-expanding or irrotational (Collins 1984) using both orthonormal and null tetrads. A discrepancy between Collins (1984) and Wolf (1986) is resolved by explicitly solving the field equations to prove that the only purely electric, shear-free, geodesic but rotating perfect fluid is the Godel (1949) solution. The irrotational fluids with shear are then studied and solutions due to Szafron (1977) and Allnutt (1982) are characterised. The metric is simplified in several cases where new solutions may be found. The geodesic space-times in this class and all Bianchi type 1 perfect fluid metrics are shown to have a metric expressible in a diagonal form. The position of spherically symmetric and Bianchi type 1 space-times in relation to the general case is also illustrated.

Prevalence and characteristics of spontaneous tinnitus in 11-year-old children

OBJECTIVE: To estimate the prevalence of spontaneous tinnitus in 11-year-old children. DESIGN: A prospective UK population-based study. STUDY SAMPLE: A total of 7092 children from the Avon longitudinal study of parents and children (ALSPAC) who attended the hearing session at age 11 years and answered questions about tinnitus. RESULTS: We estimated the prevalence of any spontaneous tinnitus as 28.1% (95% CI 27.1, 29.2%), and the prevalence of 'clinically significant' tinnitus as 3.1% (95% CI 2.7, 3.5%). Children were less likely to have clinically significant tinnitus if the tinnitus was 'soft' rather than 'loud' and if continuous rather than intermittent. Clinical significance was more likely if the tinnitus occurred more than once a week. Neither pitch nor length of history were important determinants of clinical significance. Small increases in mean hearing threshold (of up to 2.3 dB HL) were associated with clinically significant tinnitus. CONCLUSIONS: Although the prevalence of any tinnitus in 11-year-old children appears high, the small proportion in which this was found to be clinically significant implies that this does not necessarily indicate a large unmet clinical demand. We would expect approximately one child per class of 30 to have clinically significant tinnitus which is, by definition, problematic.