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We know black holes emit streams of radiation ,also recently discovered that they emit visible light when they eat any nearby matter . "We find that activity in the vicinity of a black hole can be observed in optical light at low luminosity for the first time," astronomer and lead researcher, Mariko Kimura from Kyoto University in Japan, told Charles Q. Choi at Space.com.  But it is different from what we normally hear that neither matter nor radiation can escape from black holes. So what's the reason for this.??

Abhishek Thawait
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Black hole don't allow anything to escape, if the matter/light is inside the event horizon (boundary which describes the point of no return). The emission radiation that is referred in the question is not within the event horizon, so it can escape. This is caused by friction within matter which is swirling in to the black hole.

Gauti
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What you need to understand is that a black hole is a region of space defined by an event horizon.

The key point about an event horizon is that if you're inside the region it surrounds you cannot get out. But it's only the stuff inside that is restricted in this absolute way.

If something is outside (even just outside) it can, in principle, happily orbit the black hole. And in fact we know that this is possible because the super massive black hole at the center of the milky way is known (and was identified because of) stars that orbit it (and approach very closely).

Radiation emitted by material near a black hole can, therefore, reach us.

StephenG - Help Ukraine
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    " (even just outside) it can, in principle, happily orbit the black hole." Not really true. – ProfRob Apr 05 '18 at 09:24
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    What Rob said. The closest "orbits" are in the photon sphere at 1.5 times the Schwarzschild radius, but you have to be massless to orbit there, and even then your orbit is unstable. – PM 2Ring Apr 06 '18 at 11:34