The recent black hole picture got me thinking about gravitational redshifting of light emitted near the event horizon, or in other extreme circumstances. Is there a fundamental limit to how much light can be red-shifted? I assume the wavelength has to be small enough to fit inside the universe, but is there any other limit? In either case, do we know if there’s a lot of very low energy light around? Or is it not possible to know because it’s difficult or impossible to detect?
There is the cosmic background radiation which is left over from the era after the Big Bang and is shifted to the microwave part of the spectrum.
There is no limit. Not even “small enough to fit in the universe”, since the universe is constantly expanding. Expanding faster than the light can travel.
Astronomers use the letter z to indicate the amount of Doppler shift of light. The formulae for computing it can be found here. As far as the cosmological redshift goes, z is not a linear function of the age of the universe. We see galaxies with a z of 1 at roughly half the current age of the universe, but the furthest object we can see has a z of 11.1 (every once in a while someone finds a further object so this record probably won’t stand). The light from that object has been travelling for 13.39 billion years, that is, from when the universe was only a few hundred million years old. The Cosmic Background Microwave Radiation has a redshift of about 1024 and that’s been travelling for 13.77 billion years.
Note that the CBMR had a peak in the hard UV when first emitted and now a peak in the microwave band.
Correct me if I am wrong, but it seems to me that a black hole simply has infinite red shift and as an emitter gets closer and closer to the event horizon, its red shift would increase without limit.
Radio telescopes only work down to about 10-meter wavelength, because anything longer is blocked by the earth’s ionosphere. I don’t think anybody has launched space based radio telescopes to observe longer wavelength radio waves. (There have been some space radio telescopes but those were for space-based interferometry.)
Such a space radio telescope would be challenging. Just detecting low-frequency radio waves require very long antennas, typically on the order of the wavelength you are trying to detect. So it needs a very long deployable structure, or perhaps some kind of spin-stabilized structure. And one antenna would just detect radio waves from almost every direction, so you probably want an array of satellites widely spaced to get any useful information.
Very interesting things happen at the event horizon. Extrapolating from the math, yes, the red shift appears to tend to infinity and so does gravitational time dilation, but all that really means is that the Einstein field equations break down and aren’t really meaningful at that point.
But the belief is that if you watched an object falling towards a black hole, along with the increasing red shift you would see it moving slower and slower and if you could somehow detect it at the event horizon it would appear frozen in time. This creates an interesting paradox about how anything could actually fall into a black hole, yet in the proper time of the infalling object it passes through the event horizon at a very high rate of speed (a rate of speed, in fact, that if it were accelerated from a very large distance, would approach the speed of light). There are several interesting ways of conceptually resolving that paradox. Also of interest is that the same field equations suggest that once the EH is crossed, inside the black hole the time dimension and the spatial dimension pointing to the singularity switch places. Conceptually, you can’t avoid falling into the singularity because the singularity is now your future, and you can’t escape from the black hole because there is no spatial direction that is “out”. To escape from a black hole you would have to time-travel into the past.
“What actually transpires beneath the veil of an event horizon? Decent people shouldn’t think too much about that.”
Academician Prokhor Zakharov, “For I Have Tasted the Fruit”