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CLASSICAL APPROACH TO GRAVITATION
THE COORDINATE FREE METHOD
3 other sections not shown
absence of gravitation affine parameter antisymmetric Bianchi identity Brans-Dicke theory called Cartan equation component compute connection Consider contravariant vector coordinate basis coordinate frame coordinate system coordinate transformation covariant derivative covariant vector curvature form curvature tensor curve define definition denotes density dx^dx Einstein equation Einstein gravity Einstein theory energy momentum tensor equation of motion Equivalence Principle exterior derivative field theory flat space-time follows freely falling gauge transformation geodesic equation gravitational field gravity theory harmonic gauge Hence integral invariant isotopic spin Killing vectors lagrangian Lie derivative linear matrix metric tensor Misner N-dimensional Newton Newton-Cartan theory non-linear Note obtain one-form p-form parallel transport particle photon rewritten Ricci tensor Riemannian satisfy scalar Schwartzschild radius Schwartzschild solution symmetric tangent vector tensor is given theorem torsion form trajectory transformation property vector field Weinberg Yang-Mills field