Finding and using exact solutions of the Einstein equations

The evolution of the methods used to find solutions of Einstein's field equations during the last 100 years is described. Early papers used assumptions on the coordinate forms of the metrics. Since the 1950s more invariant methods have been deployed in most new papers. The uses to which the solutions found have been put are discussed, and it is shown that they have played an important role in the development of many aspects, both mathematical and physical, of general relativity.Comment: 15 pages, LaTeX2e, aipproc.cls, invited lecture to appear in the Proceedings of ERE05 (the Spanish Relativity Meeting), Oviedo, September 2005, to be published by the American Institute of Physics. v2: Remarks on black hole entropy corrected. Other minor change

Effects of Changes in Surface Water Regime and/or Land Use on the Vertical Distribution of Water Available for Wetland Vegetation: Dynamic Model of the Zone of Aeration (Part 1 of Completion Report for Project A-023-ARK)

A mathematical model by Green, simulating one-dimensional vertical ground-water movement in unsaturated soils of the prairie region of Kansas, has been adapted for use in a wetlands environment typified by the wetlands forest of Eastern Arkansas. The model consists of two second-order, non-linear, partial differential equations and an algorithm for their numerical solution. The original model was extended to include functions for seasonal changes in transpiration and for drainage of excess precipitation. Before the addition of the two functions, the model reliability was limited to one growth season

Effects of Changes in Surface Water Regime and/or Land Use on the Vertical Distribution of Water Available for Wetland Vegetation: Dynamic Model of the Zone of Aeration (Appendix to Part 1 of Completion Report for Project A-023-ARK)

Appendix to Part 1 of Completion Report for Project A-023-AR

Local freedom in the gravitational field revisited

Maartens {\it et al.}\@ gave a covariant characterization, in a 1+3 formalism based on a perfect fluid's velocity, of the parts of the first derivatives of the curvature tensor in general relativity which are ``locally free'', i.e. not pointwise determined by the fluid energy momentum and its derivative. The full decomposition of independent curvature derivative components given in earlier work on the spinor approach to the equivalence problem enables analogous general results to be stated for any order: the independent matter terms can also be characterized. Explicit relations between the two sets of results are obtained. The 24 Maartens {\it et al.} locally free data are shown to correspond to the $\nabla \Psi$ quantities in the spinor approach, and the fluid terms are similarly related to the remaining 16 independent quantities in the first derivatives of the curvature.Comment: LaTeX. 13 pp. To be submitted to Class. Quant. Gra