Does this count as a valid problem against Einstein?s Theory of Relativity?

The x-rays detected from black holes do not come from inside the event horizon, they come from the hot disk of gas outside the event horizon.  No x-rays escape from inside the black hole itself.

No, the x-rays produced by a black hole originate from outside the event horizon.  They are produced by the friction of an accretion disk usually, in which matter from a close companion star is being drawn in due to tidal forces.  No form of matter or energy, however, can escape a black hole once it falls within the event horizon.

When a particle with an electrical charge moves in a magnetic field, it loses energy. This energy is ejected in the form of radiation. In this case, X-rays.

So when atoms (which have plenty of charged particles), are sucked in towards a black hole (Black holes have magnetic fields), they emit X-rays when they're still outside the event horizon (the point of no return). This does not constitute a breach of Relativity because the X-rays are emitted outside the black hole, not inside. X-rays can also be produced in other ways in the accretion disk, but this too is outside the actual black hole.

Edit: Of course that isn't a violation of relativity. That light cannot escape from a black hole was *predicted* by the theory of Relativity, it's not a violation of it. That the speed of light cannot change in vacuum is irrelevant, it's still sucked in by the black hole bending its pathway into the black hole, not by affecting its speed.

You need to study more about space-time and how it intereacts with gravity. Having light bend in a gravity field was predicted by relativity.
http://en.wikipedia.org/wiki/Spacetime
http://www.theory.caltech.edu/people/patricia/st101.html

Here is the answer to your question.

A black hole is properly termed a singularity because it is thought that the Pauli exclusion principal no longer holds. That is, the force of gravity overcomes the electrostatic force that prevents muon from existing in the same place at the same time. Everything gets smashed down into one giant particle....but it never really gets there.

In mathematics we have singularities too. These are points that we cannot talk about directly because the behavior of our function is undefined there.

We can only talk about what happens as we get very close to that point.

Black holes are the same way. We cannot talk about what happens inside of a black hole. We can only talk about what happens very close to it.

Black holes are so massive that they distort space and time. Most black holes rotate, and so twist space and time around with it. Light has no mass and is not actually attracted to the blackhole's mass. Light only bends under three conditions.

Refraction: This happens when light travels from a medium with one index of refraction, to a medium with another index of refraction.

Diffraction: This happens when light goes through an opening.

Gravitational lensing: This happens because the light is passing near a massive object that warps space. The light thinks it's going straight but it looks curved to us because the space it is in is curved.

Very close to a black hole, space is so warped that light cannot escape....but it doesn't realize this.

Light propagates through a medium by interacting with the electrons of the atoms of that medium. I imagine singularities do not have electrons, as they've been destroyed.

I kind if doubt light interacts with the singularity itself at all because of this. X-Rays count as light, btw.

Most of the action from a black hole comes from what's going on right outside of it.

So no, it's not violated, it's just that light always travels in a straight line with respect to the space it's in and if the space is warped light will follow it's curve because to the light, that is straight.

Doppler (or red shift) is certainly observable..though the speed of the light MAY be constant, Still, its "delivery" is slower if the tow are moving away from each other. Besides THAT the "relative" relationship, is just as good as "slowing down the light" because there is no (known) "fixed point" in space.

That said, "William", as mentioned, Gravity, and other things ALSO affect the speed of light, but I don't get it, Einstein was aware of many of these things too. So I'm not sure where the "conflict" lies.

But just to keep things straight on the "bizzarre" far-out fundamentalist "fringe" (or I would rather be known as "beyond the fringe") "fundi-troll" --as they call us-- side. There IS something that is MUCH faster than light, and that is the speed of thought. When God created the earth ---and all the other stuff-- it was was with the speed of thought! He said it, and it WAS! Instantly, everywhere! He didn't have to wait lightyears to get to the next star so He could create it. Duh!

I can hear 'em now, screaming their"disgusting groans" .. well, no , actually, I can't , Ha!

Hope this helps!