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Wald's approach to General Relativity is great and amazing. I love this textbook. He provides a modern introduction and develops all necessary contents. I enjoy it, again, I love this textbook!
Review: General RelativityUser Review - Jamie - Goodreads
Good times spent with this book as an undergrad. For about a year I don't think I was seen without it. Still, I feel I barely scratched the surface of it. Read full review
antisymmetric appendix asymptotically flat black hole Cauchy surface causal curve chapter compact components condition conjugate coordinate basis coordinate system curvature curved spacetime defined definition denote density derivative operator diffeomorphism discussed dual vector Einstein's equation energy exists finite flat spacetime follows function Furthermore gauge geometry given globally hyperbolic gravitational field Hence Hilbert space horizon hypersurface implies inertial inextendible infinity initial data initial value formulation integral isometry Kerr Killing field Klein-Gordon Lorentz manifold mass Maxwell's equations Minkowski spacetime natural neighborhood Newtonian notation notion null geodesic observer obtain orbit orthogonal orthonormal parallel transport parameter perturbation physical precisely properties quantum field region result satisfies scalar Schwarzschild solution singularity smooth spacelike spacetime metric spatial special relativity spherical stationary structure symmetry tensor field tensor of type theorem timelike curve timelike geodesics topology transformation universe vacuum vanishes vector field vector space