Dynamics of redshift/blueshift during free fall under the Schwarzschild horizon

TL;DR

This paper investigates how the frequency of signals received by a free-falling observer into a Schwarzschild black hole changes over time, considering emission processes, angular momenta, and the observer's perspective near the horizon and singularity.

Contribution

It provides a detailed analysis of redshift and blueshift dynamics during free fall, including new numerical simulations and the identification of blind zones in the sky.

Findings

Frequency can be infinite, finite, or zero near the horizon and singularity depending on angular momenta.

Emission conditions significantly affect the received photon frequency.

Multiple blind zones in the night sky appear as the observer approaches the singularity.

Abstract

We consider a free-falling observer who crosses the event horizon in the Schwarzschild background. In the course of this fall, he/she can receive signals from an object (like a star surface) that emits radiation. We study how the frequency received by an observer changes depending on the proper time on his/her trajectory. The scenarios are classified depending on whether the frequency is infinite, finite or zero near the singularity and the horizon. This depends crucially on the angular momenta of an observer and a photon. In this work we consider also emission process, and, as we show, conditions of emission strongly influence parameters of a photon, and thus received frequency. As one of our main results, we present numerical calculations showing evolution of the received frequency during the process of diving into a black hole, depending on parameters of an observer and emitter. We also analyze how a falling observer will see a night sky as he/she approaches the singularity. We show that there appear several blind zones, which were not analyzed previously.