Lines of Force of a Point Charge near a Schwarzschild Black Hole

The electric field generated by a charged particle at rest near a Schwarzschild black hole is analyzed using Maxwell's equations for curved space. After generalizing the definition of the lines of force to our curved background, we compute them numerically and graph them with the charge at $r=4M, 3M, \mathrm{and} 2.2M$. Particular attention is paid to the behavior of the lines of force near the event horizon and the smooth transition of the electric field to that of a Reissner-Nordstr\"om black hole.

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