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The gravitational shift of electromagnetic frequency in the strong fieldlimit is usually investigated under the common scenario, where the lightreceiver is far away from the central body while the emitter is in thestrong-field region of the lens. In this paper, the gravitational frequencyshift of light caused by a Reissner-Nordstr\"{o}m (RN) black hole is studiednumerically in the traditional strong-field scenario, as well as in thescenario where both the light emission and reception events happen in thestrong-field region of the black hole. In order to obtain the numerical resultsof the gravitational redshift, we first derive the exact null equations ofmotion in the RN geometry in harmonic coordinates. For a given light observer,a new numerical technique is proposed in the integration of the geodesicequations to determine the spatial position of the emitter, considering thefact that their spatial positions are not always known simultaneously. Our workmight be helpful to the related observations for probing strong gravity.

Null Gravitational Redshift by a Reissner-Nordstr\"{o}m Black Hole in the Strong Field Limit