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If Quasars are "beams" of energy exiting a super-massive black hole, in order for them to get through the black-hole's event horizon, they'd have to be traveling faster than the speed of light. My question is the following: My understanding of particle physics is still sketchy, nevertheless I think that in order for a particle to move faster than the speed of light, it must be mass-less. What particles are involved in the creation and furthermore, the mechanics of quasars?

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As far as we know, nothing moves faster than the speed of light. That goes for quasar ejecta as well, which may contain highly relativistic particles. – chase Feb 14 '14 at 13:34

The beam of energy is thought to originate outside the event horizon and be associated with an accretion disk formed by matter falling into the black hole.

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As the wikipedia article that you linked to explains in great detail, quasars are like any other regular radio galaxy. The beam of particles that originate from the "core" of the quasar (also called the radio jet) does not originate from inside the black hole (1) . There is an "accretion disk" that forms around the black hole, from which this jet is thought to emanate.

An accretion disc is a disc surrounding the central portion of the radio galaxy made of particles and gases of various chemical compositions that spiral inward toward the centre of the galaxy due to the gravitational pull. Closer to the centre, the accretion disk has extremely high temperatures and can be seen even in x-rays. It is in this region that the 'radio jet' is thought to form. Why they exist and how exactly they arise is still being actively debated.

To be absolutely clear, these radio jets emanate from all radio galaxies, and isn't restricted only to quasars. The reason quasars were thought to be different from regular radio galaxies, is because the radio jets are aimed almost directly at us, so they go through relativistic boosting (since the particles that form the jet are moving at relativistic speeds) and so have a flatter spectrum than other radio galaxies and they appear much brighter due to doppler boosting.

(1) We still don't know that there are black holes at the centre of galaxies. We have postulated it, and as far as observations have allowed us to, we have confirmed it. But (as far as I know) the closest we have got is observing the centre of a galaxy at ~ 10 times schwarschild radius, or something of that order.

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