Event horizon detection: Zenith view as seen by falling into a Schwarzschild black hole

Abstract

To visualize what is seen by an observer in curved spacetime, both general relativistic effects and special relativistic effects need to be considered. In this study, the author analytically proved that the zenith view seen by an observer falling freely into a Schwarzschild black hole (that is, the observer’s view of the point on the opposite side of the black hole) becomes enlarged, “redder,” and darker as the observer falls from an arbitrary initial rest position. An equation expressing the magnification factor of the zenith view was also derived. The derived factor characterizes the brightness and frequency of light emanated from the zenith view. Using these results, the author derived visualizations of the zenith views for various scenarios. As expressed by the derivations presented here, the moment when the observer sees the zenith view appear twice as large compared to the initial rest position coincides with the crossing of the event horizon; that is, a freely falling observer can detect the horizon through the simple procedure of continuing to observe the zenith view. This result implies that the effect of aberration dominates the effect of light deflection while the observer is falling.