Electrodynamics in curved spacetime: 3 + 1 formulation

This paper develops the mathematical foundations for a companion paper on 'Black-Hole Electrodynamics'. More specifically, it re-expresses the equations of curved-spacetime electrodynamics in terms of a 3 + 1 (space + time) split, in which the key quantities are three-dimensional vectors (electric field Ḛ, magnetic field |$^B_\sim$|⁠, etc.) that lie in hypersurfaces of constant time t. Three-dimensional vector analysis is used to express Maxwell's equations, the Gauss, Faraday and Ampere laws, the Lorentz force law, and the laws of energy and momentum conservation in forms closely resembling their flat-spacetime counterparts.

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