What happens to the light of a rocket falling toward an event horizon as observed from afar?

As a rocket approaches an event horizon, such as that around a black hole, the light emitted by or reflected off the rocket experiences significant gravitational redshift due to the intense gravitational field. This effect is a result of the way gravity influences the fabric of spacetime, which leads to the stretching of light waves.

As the rocket falls closer to the event horizon, the wavelengths of light it emits stretch increasingly, causing the light to shift towards longer wavelengths—specifically, into the red part of the spectrum. If the rocket continues to fall beyond a certain point, the light may become so redshifted that it effectively drops out of the visible spectrum and becomes undetectable with standard instruments. This extreme redshift means that observers far away can no longer see the rocket, as the frequency of the light decreases beyond what can be detected.

Thus, the phenomenon of gravitational redshift explains why the light from the rocket becomes undetectable as it approaches the event horizon. This concept is a key aspect of general relativity and illustrates the dramatic effects that strong gravitational fields can have on light.