Watsisname, interesting. So in order for a photon to escape from inside the event horizon, it would have had to be omitted in a very narrow window of time, and even then, the red-shift alone would make it almost impossible to detect.
Precisely. If emitted very close but just above the horizon, then it is detected almost an eternity later, with such feeble energy and long wavelength as to be a ghostly whisper of radio. If emitted very close but just below the horizon, then it pulled into the singularity, never to be known to anyone in the external universe. And if it was emitted very close and just above the horizon, but in a direction not close enough to directly outward, then it still is pulled in.
So what about the light from the star itself, as it collapsed to form the black hole in the first place? It's a very bright surface, to be sure. Being trapped in time for the distant observer, would it help provide light from the event horizon later? Even in the sense of the occasional random photon?
The thing is, the same effect which is causing the star surface to be frozen in time as it collapses is also redshifting it to invisibility. And it happens fast
. It's really quite astounding how fast it is, so let's put numbers to it. Suppose it's our own Sun collapsing to become a black hole (it won't, but let's just say it did.) How long would it take for the luminosity, as seen by the distant observer, to drop from the Sun's present value (3.85x1026 watts) to just one watt? Solution: About 1.6 milliseconds! T
he fade to black is faster than the blink of an eye!
Why? When we run through the mathematics of the collapse using general relativity, it turns out that the gravitational redshift causes the observed luminosity of the collapsing star to drop exponentially
. Exponential functions are very fast, and in this case, when the collapsing star is close to its Schwarzschild radius (where the event horizon forms), the luminosity drops by a factor of e (2.71828...) for each 26 microseconds for each solar mass of material in the collapse. To go from one solar luminosity to one watt is 61.2 reductions of e (the natural log of 3.85x1026
is 61.2), and 61.2 times 26 microseconds is 1.6 milliseconds.
This calculation makes the assumption that light is continuous and we can divide it up in to arbitrarily many little bits. But it's not -- light is actually quantized. That makes it even worse. There are only so many photons that can escape. After about 1 millisecond, the last photon that will ever escape the star's surface is seen by the distant observers. After that, it is truly black.
Some might also ask of the light of Hawking radiation. But for any black hole massive enough to be meaningful (not a "micro black hole" with less than the mass of a planet)... it's ridiculously dim. The wavelength of the photons is comparable to the diameter of the hole, and the power emitted is like that of an object near absolute zero. For a solar mass black hole, it radiates with 9x10-29
watts, which is pretty much zero. The intensity of the cosmic microwave background radiation is blindingly bright compared to it.
So yes, even while making a quip, I'm quite serious when I say it is the blackest black that was ever black.
The blackness of #000000 on your monitor is not even close -- the screen still emits thermal radiation, and even if you discount that, it still reflects a small amount of ambient light. There is no material in nature as dark as a black hole's event horizon. Not the darkest coal, not a starless night sky, not even that weird Vantablack
It's absolutely my pleasure. Black holes are amazing things.
Thanks for addressing my questions