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

TL;DR

This paper investigates the gravitational frequency shift of light caused by a Reissner-Nordström black hole in both traditional and strong-field scenarios, using numerical methods to derive null geodesics and analyze redshift effects.

Contribution

It introduces a new numerical technique for integrating geodesic equations in RN geometry, enabling analysis of redshift when both emitter and receiver are in strong gravity regions.

Findings

Numerical results for gravitational redshift in strong-field scenarios.

Development of a method to determine emitter position without simultaneous spatial knowledge.

Insights into gravitational redshift behavior near charged black holes.

Abstract

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