By slightly useless I mean passing through the double cover. Physical space times are not conformally flat. So the construction via the double cover is not useful for understanding physical spacetimes.

For your second question: as I wrote in the text, parametrize by and then is exactly the subset . The action is .

For your third question: can’t help you there. Penrose’s construction is not useful for the types of problem that is usually treated in mathematical GR (from the evolutionary PDE point of view), so the sources I know will tend not to discussion it. I write it down here more as an intellectual curiosity

]]>Again, thanks.

]]>Second, and if I may beg a little patience, how exactly does the double cover work? M’ is a double cover of the image of Minkowski space by which map? Is there a Z/2 group action that identifies the fibres?

Is there a handy reference that discusses the mathematics of this, rather than that LR article? The physics, while it rings a bell from ages past, is not meaningful to me, so even discussions of Penrose diagrams slows down the process, I’m afraid.

Many thanks for writing this, since it has been the only reference I’ve found so far that actually deals with the manifolds in question, and not merely metrics or physics.

]]>Thanks

Dianne ]]>