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The Electromagnetic Field of a Known Charge Distribution
The Field in the Presence of Conductors
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1-forms acceleration affine connections asymptotic calculate Cauchy surface causal curve co's codifferential components conservation constant contribution convergence coordinates Cosh covariant derivative curvature forms defined direction Einstein's equations electric field electromagnetic electron energy and momentum energy density energy-momentum forms energy-momentum tensor example exterior differential factor field equations Figure finite formula Fret geodesic vector field gravitational energy gravitational field Green function hence implies infinite infinity integral integrand invariant Isotropic Spaces Killing vector fields Lagrangian Lie derivative light-cone linear manifold Maxwell's equations Minkowski space motion natural basis orthogonal basis particle Penrose diagram point charge potential Problem produces radiation relativistic Remarks satisfies scalar Schwarzschild metric sin2 singularity Sitter universe solution spacelike speed of light spherical submanifold symmetric term theorem theory timelike total energy transformation vanish wave world-line zero