Behavior of null-geodesics in the interior of Reissner-Nordstrom black hole

TL;DR

This paper analyzes the behavior of null-geodesics inside Reissner-Nordstrom black holes, revealing how they cross horizons and approach the inner horizon, and constructs a geometric optics solution related to these geodesics.

Contribution

It provides a detailed analysis of null-geodesic trajectories within Reissner-Nordstrom black holes and constructs a geometric optics solution associated with these paths.

Findings

Null-geodesics cross outer and inner horizons.

Geodesics turn inside the inner horizon and approach it asymptotically.

Constructed a geometric optics solution supported near the null-geodesic.

Abstract

We show that an incoming null-geodesic belonging to a plane passing through the origin and starting outside the outer horizon crosses the outer and the inner horizons. Then it turns at some point inside the inner horizon and approaches the inner horizon when the time tends to the infinity. We also construct a geometric optics solution of the Reissner-Nordstrom equation that has support in a neighborhood of the null-geodesic.