The potential of a static electric charge located in a Schwarzschild gravitational field is given by Linet. The expressions for the field lines derived from this potential are calculated by numerical integration and drawn for different locations of the static charge in the gravitational field. The field lines calculated for a charge located very close to the central mass can be compared to those calculated by Hanni–Ruffini. Maxwell equations are used to analyze the dynamics of the falling electric field in a gravitational field.
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Harpaz, A. Electric Field in a Gravitational Field. Found Phys 37, 763–772 (2007). https://doi.org/10.1007/s10701-007-9118-8
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DOI: https://doi.org/10.1007/s10701-007-9118-8