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General Relativity

Falling through the Event Horizon

The passage of time we experience is not the same as the passage of time experienced by other objects. In special relativity, an observer at rest and an accelerating observer see each other's clock move at a different rate than their own. For example, an observer on Earth sees the clock of a traveler accelerating away from Earth slowing, while conversely the traveler sees the observer's clock slowing.

The appearance of an object falling through the event horizon of a Schwarzschild black hole—we won't be so cruel as to drop an observer onto our black hole—to someone hovering stationary above the black hole is similar to the appearance of Earth to the accelerating traveler, with the similarity becoming more identical the closer the person hovers to the event horizon. The deviations that do occur from the event horizon of special relativity arise because of tidal forces within the gravitational field—the gravitational field of a Schwarzschild black hole is spherically-symmetric around the point mass, so the direction of the force changes with changes in position. For small objects close to the event horizon, this tidal effect is negligible, and the physics around this event horizon becomes identical to that around an event horizon in special relativity.

What the hovering person sees is quite different from what the free-falling objects sees. As the free-falling object approaches the event horizon, the hovering person sees the object move more and more slowly. If a clock is moving with the object, the person sees the pace of the clock's ticking slow. Light from the object is Doppler shifted to lower frequencies, and the intensity of the light from the object falls. But the person never sees the object reach the event horizon; the object simply continues to slow and grow dim, as though it were a physical manifestation of Zeno's paradox—always approaching, but never reaching, the event horizon.

To the object, the event horizon is unremarkable; as recorded by the object's clock, the object not only reaches the event horizon in a finite amount of time, it continues past it in a finite amount of time. What the objects sees is also unremarkable: the hovering person remains visible as the object travels through the event horizon. The person will appear to be accelerating away from the object, so the light from the person will be Doppler shifted to lower and lower frequencies, and it will be less and less intense.

It is the acceleration of the hovering person that gives the event horizon its physical meaning to the falling object. As the person accelerates away, the object sees it move closer and closer to the speed of light. At some point, the velocity of the observer is so close to the speed of light that light emitted by the falling object can never catch up. Time, or events, experienced by the object after this point cannot affect the hovering person, so the object has passed through the “event horizon” for the accelerating, hovering person. Inside the event horizon, the object experiences a passage of time that, as measured by the hovering person's clock, takes it to infinity and beyond.

Besides the different views of each other, the hovering person and the free-falling object see the world around them differently. Starlight falling onto the black hole appears Doppler shifted to high frequencies to the hovering person, with the amount of Doppler shift dependent only on the distance of the hovering person from the center of the black hole. These stars, however, would appear crowded towards his zenith, and he would feel as though we were at the bottom of a giant black bowl, or an urn if he is close enough to the event horizon, with the edge of the bowl set by the disappearance of stars on the sky. The edge of this bowl is set by the distance from the event horizon, with the angle from the zenith to the edge getting smaller as the person moves towards the event horizon. At the event horizon, the sky compresses to a single point at the zenith, and the remainder of the sky is black. Why this should be so is straightforward: the closer the person is to the event horizon, the greater the rate at which he must accelerate, so that at the event horizon, the acceleration rate is infinity; this acceleration makes everything falling to the event horizon appear to move at nearly the speed of light perpendicular to the event horizon, making starlight appear to come from the zenith.

An object falling into the black hole, however, sees starlight as Doppler shifted to either higher or lower frequencies, depending on the direction the light comes from. For instance, an object falling radially into the black hole sees the starlight from directly above as Doppler shifted to the red, but it sees the starlight coming from the sides and forward as Doppler shifted to the blue. Above the event horizon, the object's sky always extends from the zenith by more than 90°. This gives the object the impression of always hovering over a black pit in the sky. Even at the event horizon, the zenith angle to the edge of the black hole is 138°. As far as the object is concerned, it is far above the event horizon despite being at it.

The hovering person sees the event horizon covered by a dense, nearly motionless, and nearly black layer of gas collected over billions of years, but the free-falling object sees these things moving well ahead of it. If two objects fall through the event horizon together, with one just ahead of the other, the hovering person will see them as coming closer together as they approach the event horizon, but these object will see themselves maintaining a nearly constant separation in space (the tidal forces causes a very slight increase in separation).

Event horizons are strange, but they are strange because of the properties of special relativity. The one feature that black holes add to them is that they hold the event horizon in place, because they are defined by observers hovering in place within the black hole's gravitational field.

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