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The escape velocity at event horizon of a black hole is same as speed of light, So this questions is not about all photons travelling into a black hole, but for those which are tangential to the event horizon, So let us assume that a photon is travelling along a tangent to event horizon, we know that gravitational force of black hole will bend the space and make the photon to orbit black hole just at the boundary of event horizon. It will never fall into black hole but it will never escape. So my question is if there are infinite number of photons trapped at event horizon(Those photons may be trapped right after the birth of black hole), If a bot is to travel at event horizon, It can see images of distant and very very old celestial bodies.

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    $\begingroup$ The event horizon would be an unstable point in classical physics, it's dissipative because of gravitational waves in GR, it will leak past the event horizon because of the wave nature of light in both electromagnetism and quantum mechanics, so I can think of at least four reasons to say, "no, there are no such photons". $\endgroup$ – CuriousOne Jun 7 '15 at 9:12
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For a non rotating spherical black hole the event horizon is at a circle of circumference $4\pi MG/c^2$. And gravity gets weaker the farther away you get.

At that location even moving straight outwards at light speed won't let you travel to someplace where gravity is weaker.

But if you aren't moving straight away then you will get trapped even farther out. For a non rotating spherical black hole the photon sphere is at a circle of circumference $6\pi MG/c^2.$ At that location you can go in a circle at light speed, but if you get any closer then even going sidewise at light speed you will spiral inwards.

So the photon sphere is the ball around which even light can't orbit. But the event horizon is where light heading outwards can't escape the gravity if the black hole.

In between the two you can escape but you can't orbit.

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