Lecture notes that derive the nonlinear Einstein field equations from the gravitational action and apply them to black holes, cosmology, and gravitational waves at the advanced undergraduate level.
Hirata.http://www.tapir.caltech.edu/ ~chirata/ph236/lec08.pdf
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A short course in general relativity
Lecture notes that derive the nonlinear Einstein field equations from the gravitational action and apply them to black holes, cosmology, and gravitational waves at the advanced undergraduate level.