If nothing can come out of the black hole, how come the x-rays can be emitted?
Black holes that exist near other stars attract a great deal of gas from the neighboring star toward the black hole. This gas gets accelerated to extremely fast speeds and friction within the gas streams causes it to heat up to temperatures high enough to emit X-rays.
These X-rays are emitted outside the event horizon of the black hole. If you think of a black hole as a bottomless hole that nothing can ever possibly escape from, then the X-rays do not come from inside the hole but from just near the edge of it.
Radio and X-rays can also be emitted simply by mass that's been accelerated greatly by the black hole escaping its influence and racing off in some other direction (often near the speed of light).
Ted Pavlic, B.S., Electrical Engineering Grad Student, Ohio State
The x-rays you are asking about does not come directly from the black hole itself, but from material being heated as it falls in to the black hole.
Some black holes are thought to have accretion disks. There are disks of dust, gas and anything else it can capture. These swirl around and heat up as they get sucked in. This heat is radiated away from the black holes and we see it as x-rays.
Black holes do however have there own temperature. Berkenstein realised that black holes themselves have entropy. This is however a violation of the second law of thermodynamics. Remember, that it was thought that black holes have no temperature. Hawking realised that if black holes were hot, then there is no violation.
This is the famous Hawking temperature
T = k/m
where k is a small constant and m is the mass of the black hole. This means that astronomical black holes have a very low temperature.
The radiation emitted in this way carries away energy from the black hole. Using E=mc^2, we see that the black hole loses mass. This is Hawking radiation and black hole evaporation.
However, one difficulty remains. A black hole can be characterised only by its mass, angular momentum and electric charge. Classically black holes are not complicated, entropy is a measure of missing information. But where does this missing information come from? This is the starting point for the Hawking entropy/information paradox.
Hawking has proposed a solution to this just recently. He suggests that in fact using quantum gravity only virtual horizons exist which can leak information and the paradox does not exist. This is ok, but doesn't point to a classical understanding of this. I mean the original problem is a classical one, but the solution a quantum one. Not everyone is happy about Hawking's solution!
Andrew James Bruce, Physics Grad Student, UK
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