Event horizon pileup

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Question:

I understand that because of time dilation that we could never see something actually entering a black hole. That is to say, from our earth view, time would appear to stop at or near the event horizon and observed objects would appear to move slower and slower until they seemed to be standing still (to be clear, I certainly understand that the object does not actually halt its motion, and will continue to accelerate and fall into the hole). I understand (laymans level) the basic concept of time dilation, and that it is how the speed of light remains constant for all observers, but the idea of something appearing to halt its motion is pretty mind-blowing...I picture (when it becomes technically possible to actually see one) an event horizon cluttered with incoming matter but that matter never descending (according to our observation) into the black hole. That seems far fetched to me, so I am sure I'm missing something.

Answer:

You are right to think that the idea of seeing objects piled up at the event horizon of a black hole seems far-fetched. When an object falls toward the event horizon of a black hole, it does slow down and eventually appear to stop outside the event horizon. However, the object also becomes too dark too see before it appears to stop moving. Because of the darkening, you would never actually see a pileup of objects near the event horizon. To understand why the darkening occurs, it is useful to think about what happens to light that travels from the object to a distant observer on Earth. Light can be described both as a wave and as a bunch of particles, so we will consider both descriptions.

First we imagine a wave of light being emitted from our doomed object. When a wave source and an observer are moving relative to one another, the observer detects the wave at a different frequency than the frequency the source emits. This phenomenon, called Doppler shift, is why cars sound high-pitched when they are moving toward us and low-pitched when they are moving away. As our object approaches the event horizon, it is moving away from us faster and faster and approaching the speed of light. The Doppler shift increases with the object's speed, and we see a lower and lower frequency wave.

Next we turn to the particle description of light. All particles have to use up energy to escape the pull of gravity. Light particles, called photons, are no exception. Any photon emitted from our object will lose energy as the photon travels out of the black hole's sphere of gravitational influence, toward an observer on Earth. The photon loses a greater fraction of its energy traveling away from the black hole the closer to the event horizon it is emitted.

Now our two views of light become one again. Lower frequency light waves consist of lower energy photons, so both views of light give us the same observable change. We can only see a small range of light frequencies with our own eyes, called the visible spectrum. Eventually all of the light coming from the object would have a lower frequency than our visible range, and the object would disappear.

The problem becomes more interesting if we consider that telescopes allow us to see a much greater range of frequencies. In fact there is no limit on the lowest frequency we can theoretically observe. This leads to the question: as the frequency of the light waves decreases, can we just keep switching to telescopes that observe lower frequencies and continue to observe the object? This is possible in theory, but not very practical. Lower frequency light waves have longer wavelengths, and a telescope has to be larger than the wavelength of light it is trying to observe to produce a clear image. Eventually the light that gets to us will have a wavelength longer than our largest telescope and we will not be able to produce a clear image of the object. We could try to build bigger telescopes while we observe it, but this would be a tough feat considering the wavelength of light increases exponentially with time. The larger the black hole, the more gradually objects fade away as they fall into it. To continually observe an object near the event horizon of one of the largest supermassive black holes, we would have to build a ten-fold larger telescope about every few months. Still, if we started with the largest telescopes we have today, in about a year we would need a telescope larger than the earth. In a few years, we would need a telescope bigger than our solar system.

--Alex Wise