If nothing can escape a black hole, where does Hawking radiation come from? Hawking radiation is a form of electromagnetic wave travelling at the speed of light. Hawking radiation is radiated from a black hole. If nothing can escape the gravitational pull of a black hole, how can Hawking radiation do so?
 A: Nothing can escape a black hole Once it has crossed the event horizon. Quoting from the wikipedia  article 

Physical insight into the process may be gained by imagining that particle-antiparticle radiation is emitted from just beyond the event horizon. This radiation does not come directly from the black hole itself, but rather is a result of virtual particles being "boosted" by the black hole's gravitation into becoming real particles.[10] As the particle-antiparticle pair was produced by the black hole's gravitational energy, the escape of one of the particles lowers the mass of the black hole.[11]
An alternative view of the process is that vacuum fluctuations cause a particle-antiparticle pair to appear close to the event horizon of a black hole. 
  One of the pair falls into the black hole while the other escapes. In order to preserve total energy, the particle that fell into the black hole must have had a negative energy (with respect to an observer far away from the black hole). This causes the black hole to lose mass, and, to an outside observer, it would appear that the black hole has just emitted a particle. In another model, the process is a quantum tunnelling effect, whereby particle-antiparticle pairs will form from the vacuum, and one will tunnel outside the event horizon.

So, the radiation that is being emitted can be thought of as  originating from just outside the event horizon.
