I'm looking for a rigorous exposition of Penrose diagrams (also called conformal diagrams in general relativity. By "rigorous" ("careful" is perhaps a more attractive word) I mean that it should address the following questions:
- Is there a general mathematical definition of a Penrose diagram? If spacetime is not 2-dimensional, what kind of symmetries do we need to construct a diagram?
- Given a 2-dimensional metric, is the Penrose diagram unique?
- How are infinities (timelike, null, spacelike) formally defined? Can they be defined without appealing to the conformal diagram?
I'm thinking there should be an article, book or something like that covering this, but if this can be answered right here in this site, by all means.