What are some good books, lecture notes, articles, etc. that can be used as introduction to the landscape of major results in general relativity since Einstein? In terms of the timeline, I'm thinking anything starting from around the Kerr solution and Penrose's singularity theorem.

For some context, I'm a mathematician and so am really looking for the application of differential geometry beyond basic Riemannian geometry and how other areas like topology and spinors have found their way into GR.

I would also be very interested to see literature focused on the application of GR to astrophysics. Particularly, what has been done beyond numerical analysis.



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These notes from an applied mathematics course on GR by David Tong http://www.damtp.cam.ac.uk/user/tong/gr/gr.pdf provides beyond the basic theory, some short interludes into the more advanced/modern topics in both the physics and math.

Examples include "a sniff of Hodge theory," "the relation to Yang Mills theory," "confromal transformations," and "the no hair theorem."


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