General Relativity (GR), just like electromagnetism, has two degrees of freedom per space point. It is important, for problems ranging from numerical relativity to quantum gravity, to explicitly identify these degrees of freedom. While it is possible to mimic the electromagnetic analysis in the weak field case, life is much more complicated when the gravitational field is strong. One reason is the nonlinearity of the Einstein equations, another (even more significant) is the central role of the gauge fields in GR While electromagnetism is a gauge theory, we can write the Maxwell equations entirely in terms of the electric and magnetic fields, which are gauge independent. In GR, the metric is a gauge variable, the direct analogue of the vector potential in electromagnetism, and it cannot be eliminated from the field equations. The only really successful attack to date has been the conformal method. This talk will give an overview of this approach. Constant mean curvature foliations (`York time') and the Lichnerowicz-York equation will emerge as the key elements in analysing GR as a dynamical system.
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Last updated April 29, 2004. This page was created and is maintained by Stephen Wills (s.wills@ucc.ie).