Conformal Approach and Its York Time

Abstract

This chapter is about the further conformal approach to general relativity’s constraints. This works for maximal and constant mean curvature spatial slices, and leads to further configuration spaces for general relativity: conformal Riem and conformal superspace. While maximal slicing is frozen for closed spaces, constant mean curvature slices can be interpreted in terms of an internal or hidden time: York time. Scaled relational mechanics has a partial analogue of this: Euler time. Both are dilational momentum quantities and have sizeable regimes in which monotonicity is assured. York time, moreover, has the further distinction of requiring a ‘fixing equation’ which extends a given constant mean curvature slice to at least a local foliation’s worth of such surfaces.