General theory of relativity
Einstein's general theory of relativity requires a curved space for the description of the physical world. If one wishes to go beyond superficial discussions of the physical relations involved, one needs to set up precise equations for handling curved space. The well-established mathematical technique that accomplishes this is clearly described in this classic book by Nobel Laureate P.A.M. Dirac. Based on a series of lectures given by Dirac at Florida State University, and intended for the advanced undergraduate, "General Theory of Relativity" comprises thirty-five compact chapters that take the reader point-by-point through the necessary steps for understanding general relativity.
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action density action principle antisymmetric becomes Bianci relation change of coordinates charged matter Christoffel symbol coefficient components condition conservation constant contravariant vector coordinate system corresponding covariant derivative covariant differentiation covariant vector curved space curvilinear coordinates d'Alembert equation denote distribution of matter downstairs suffix dx1 dx2 dx3 Einstein equations Einstein's law electromagnetic field empty space energy and momentum equations for empty expression field equations field quantity flat space formula four-dimensional function gives gravitational field gravitational waves harmonic coordinates Hence hold invariant Lagrangian law of gravitation Let us suppose Let us take lower suffixes MATERIAL ENERGY TENSOR metric multiply Newtonian approximation nontensor number of dimensions oblique axes parallel displacement particle pseudo-tensor rectilinear result Ricci tensor right-hand side satisfies scalar field Schwarzschild solution second derivatives Section shift special relativity static symmetrical system of coordinates term theorem timelike track upstairs vanishes velocity of light world line zero