That is what the parent comments were talking about - on the photon sphere - in case of a non-rotating black hole - photons could theoretically orbit the black hole but as pointed out by your parent comment this orbit is not stable and any tiny perturbation will either send the photons into the black hole or make them escape. And the photons would of course not stand still - they are massless particles and therefore can only move at the speed of light, neither slower nor faster - but orbit the black hole at the speed of light.
If you were further in the black hole’s gravity well than the photons in the photon sphere, you would see them redshift and eventually freeze, right? I.e. from inside the photons don’t appear to escape
There are no frames of reference where photons reverse direction. If everything is spherically symmetric, a photon emitted from any point in spacetime is either (1) already heading outward and escapes or (2) already heading inward and is consumed. Within the event horizon, only trajectories of type (2) exist. The picture of a photon struggling outward to escape and then reversing direction under gravity is incorrect.
Ok, thanks for bringing precision to my comment. It makes sense that any photons reaching an observer who is inside a BH event horizon must also already be trapped inside the EH.
I think what I find confusing is that I thought outside observers would never see the infalling observer reach or cross the EH due to time dilation.
I’ve read that an observer falling into a black hole would notice extreme time compression in the external universe (observing millions or billions of years pass in the external reference frame), and conversely external observers would notice extreme time dilation of people and redshifting of photons falling into the black hole. Infalling particles from their external perspective appear frozen and smeared into a blur outside the EH, fading away but never optically appearing to “enter” into the BH, even though physically these particles indeed have/will.
So I think I had it backwards, the external observers would see infalling objects redshift, and those falling in would see the universe blueshift (I guess getting fried by high energy photons before being torn up by tidal forces).
> I think what I find confusing is that I thought outside observers would never see the infalling observer reach or cross the EH due to time dilation.
It depends what you mean by "see". An outside observer will certainly not see this this in the literal sense of seeing photons that image the horizon-crossing event. However, there are sets of space and time coordinates on the manifold where the infalling observer crosses the horizon at the same "time" as external events occur.
> frozen and smeared into a blur outside the EH, fading away but never optically appearing to “enter” into the BH
Yes, but note that the brightness of the image gets exponentially suppressed as the infalling object approaches the horizon, so it really just looks more like it's vanishing than freezing (although it's doing both). Importantly, a finite amount of electromagnetic energy is emitted/reflected by the infalling object before it crosses the horizon so, for any given minimum-energy threshold of your detection equipment on the outside, you will see no more than a certain finite number of photons no matter how long you wait.
> and those falling in would see the universe blueshift (I guess getting fried by high energy photons before being torn up by tidal forces).
No, I don't think much blueshifting happens. If you hover above the event horizon of a black hole, the outside world will look blueshifted, to a stronger and stronger degree as you get closer to the horizon. However, the amount of force necessary to maintain a stationary position above the horizon goes to infinity as you get close, so you can't get arbitrarily close and experience arbitrarily large blueshift; indeed, the blueshift is in general quite modest without extraordianry materials or fuels. And once your support fails, so that you start falling into the black hole, the blueshifting goes away.
