What is the Structure of Classical General Relativity?

[wolram]

http://arxiv.org/PS_cache/gr-qc/pdf/0506/0506065.pdf

Title: Classical General Relativity
Authors: David B. Malament
Comments: 59 pages; 7 figures; to appear in Handbook of the Philosophy of Physics, eds. J. Butterfield and J. Earman, Elsevier

This survey paper is divided into two parts. In the first (section 2), I give a brief account of the structure of classical relativity theory. In the second (section 3), I discuss three special topics: (i) the status of the relative simultaneity relation in the context of Minkowski spacetime; (ii) the "geometrized" version of Newtonian gravitation theory (also known as Newton-Cartan theory); and (iii) the possibility of recovering the global geometric structure of spacetime from its "causal structure"

 

[dextercioby]

Thank you,a very useful lecture,indeed.I don't have time right now to get through the calculations,so i'll let others share their comments.

Daniel.

 

[pervect]

http://arxiv.org/PS_cache/gr-qc/pdf/0506/0506065.pdf

Title: Classical General Relativity
Authors: David B. Malament
Comments: 59 pages; 7 figures; to appear in Handbook of the Philosophy of Physics, eds. J. Butterfield and J. Earman, Elsevier

I think there may be some interesting insights buried in this paper, but reading it I feel like I'm being tied up in fibre bundles (note: that's a bad pun, not to be taken too literally).

 

[robphy]

The notation is similar to Wald's notation.

Here are some of the good parts IMO (not usually found in standard treatments):

2.3 Space/Time Decomposition at a Point and Particle Dynamics shows how to calculate using 4-vector quantities.
2.5 Einstein’s Equation and 3.2 Geometrized Newtonian Gravitation Theory discusses a spacetime formulation of Newtonian Gravity
3.1 Relative Simultaneity in Minkowski Spacetime discusses the "definition of simultaneity"
3.3 Recovering Global Geometric Structure from “Causal Structure” may play an important role in recovering spacetime structure from causal-structure-based attempts to quantum gravity.

If you google the author, you'll find some more detailed course notes.