TITLE: The independent gravitational degrees of freedom

SPEAKER: Professor Niall Ó Murchadha

General Relativity, just like electromagnetism, has two degrees of freedom per space point. One consequence is that gravitational radiation, just like light, has two independent polarizations. It is important, for problems ranging from numerical relativity to quantum gravity to identify the dynamical degrees of freedom of the gravitational field. While it is possible to mimic the electromagnetic analysis in the weak field case, in the strong field case life is much more complicated. One reason is the nonlinearity of the Einstein equations, another (even more significant) is the central role of the gauge fields in general relativity. While electromagnetism is a gauge theory, we can write Maxwell's equations entirely in terms of the electric and magnetic fields, which are gauge independent. In general relativity, the metric is the direct analogue of the vector potential, and it cannot be eliminated from the field equations. This talk will show, with as little technical detail as possible, how these difficulties can be surmounted.