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In recent simulations of what a black hole would actually look like (for example, the images made in the production of the movie Interstellar using data provided by Kip Thorne) the event horizon is defined by a "shadow." I understand that the Event Horizon Telescope is going to attempt to capture an image of the "shadow" (which is extremely exciting). But I understand that there are photons that are temporarily trapped in orbits around a black hole, some of which escape and some of which fall into the black (Kip Thorne refers to this a the "Shell of Fire"). If this so, why is a shadow visible? Would not the so-called shell of fire make the black hole appear to be bright? Or are the photons "invisible" until they escape and hit an observer's eye?

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Or are the photons "invisible" until they escape and hit an observer's eye?

Exactly. Simply put,the photons that reaches our eyes is what we see;if they do not reach our eyes,we do not see them. Light has to hit the light-sensitive retina at the back of our eye before we can see it. Same reason why a black hole is black;there are no photons "reflecting off the surface" of a black hole and hitting our eyes. The definition of the event horizon is basically the point where even light cannot escape, so we simply cannot see it.

Would not the so-called shell of fire make the black hole appear to be bright?

No,since the photons orbiting it do not hit our eyes (assuming the observer is not at the photon sphere). However,those that escape and manages to hit our eyes would be visible.

why is a shadow visible?

A shadow is not visible in the strict definition (visible = able to be seen) We see something because light reflecting off it or being emitted by it reaches our eyes;a shadow is

partial or complete darkness

and darkness cannot be seen, it is simply the lack of light. We instead see the brighter surrounding area and not (or see less of) light in the darker area (called the shadow)

I suppose the "shadow" referred to here is the region of darkness surrounded by bright light from the accretion disk? Actually if so,the word "shadow" is not accurate considering the conventional definition

a dark area or shape produced by a body coming between rays of light and a surface

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