The bag of gold reopened

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Abstract
The standard way to construct initial data for general relativity is by means of a conformal transformation, which brings one from the space of freely specifiable data to a solution of the constraints. The major difficulty with this technique is that the conformal factor may not be everywhere positive. When the conformal factor passes through zero, the initial data generated by the conformal transformation possess a singularity evocatively called a bag-of-gold singularity by J A Wheeler (1974). In the asymptotically flat case, the boundary between good free data and the rest consists of points which do not generate asymptotically flat solutions to the constraints, rather the conformal factor goes to zero at infinity and one gets a regular compact solution. On one side of the boundary the ADM energy blows up to + infinity , on the other side, where we have the bags of gold, the energy shrinks to - infinity . This means that one can use the ADM energy as a Morse function on the set of good solutions to the constraints and so describe its topology.