Hobson M.P., et al. General relativity (An Introduction for Physicists)

Cambridge University Press, 2006. - 572 p.The spacetime of special relativity
Manifolds and coordinates
Vector calculus on manifolds
Tensor calculus on manifolds
Special relativity revisited
Electromagnetism
The equivalence principle and spacetime curvature
The gravitational field equations
The Schwarzschild geometry
Experimental tests of general relativity
Schwarzschild black holes
Further spherically symmetric geometries
The Kerr geometry
The Friedmann–Robertson–Walker geometry
Cosmological models
Inflationary cosmology
Linearised general relativity
Gravitational waves
A variational approach to general relativity