Let's look at what is considered to be an important claim in Stephen Crothers' refutation of black hole cosmology: "Black Holes violate General Relativity".

Consider a cuboid rest-mass \(m_0\) of sides length \(x\). Let it move with constant rectilinear velocity \(v\) in the x-direction. Its mass is given by: $$m=\frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$$ and its volume is given by:  $$V=x^3 \sqrt{1 - \frac{v^2}{c^2}}$$ So the density D of the moving mass is: $$D=\frac{m_0}{x^3 \sqrt{1 - \frac{v^2}{c^2}}}$$ which is infinite when \(v \to c\)  but this is forbidden by Special Relativity since no material object can travel at the speed of light in vacuo. So infinite densities are forbidden by Special Relativity. Now the so-called "point-mass" has a finite mass and a zero volume, so that it is infinitely dense, which is what the singularity of the alleged black hole is supposed to be. Thus, if General Relativity permits point-masses it does so in violation of Special Relativity. Yet General Relativity is supposed to be a generalization of Special Relativity to non-uniform motion. It cannot therefore violate Special Relativity. So if General Relativity is to be consistent with Special Relativity, it cannot permit point-masses, howsoever they are alleged to be formed, despite what Prof. Mr. Krasinski et al. might otherwise and vagariously claim. [1]

Stephen Crothers do a common error here, and it's about "relativistic mass", he doesn't even precise what he means by the term mass. Its use is quiet meaningless, i.e. the mass of a body does not increase with velocity. So the use of the relativistic mass equation when refuting infinite densities is wrong. Quoting Igor Ivanov [2]:

The mass (the true mass which physicists actually deal with when they calculate something concerning relativistic particles) does not change with velocity. The mass (the true mass!) is an intrinsic property of a body, and it does not depends on the observer's frame of reference. I strongly suggest to read this popular article by Lev Okun, where he calls the concept of relativistic mass a "pedagogical virus".

What actually changes at relativistic speeds is the dynamical law that relates momentum and energy depend with the velocity (which was already written). Let me put it this way: trying to ascribe the modification of the dynamical law to a changing mass is the same as trying to explain non-Euclidean geometry by redefining π!

So the real equation is: $$D=\frac{m_0}{x^3}$$
Where the density becomes infinite when \(x  \to 0\) , so it doesn't violate Special Relativity nor General Relativity since it doesn't imply that a material body reach the speed of light in vacuum.
That's the first point.
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Stephen Hawking said: "There should be an infinite dense point-mass singularity at the centre of a black hole." That means that there should be an infinitely dense point-mass (mathematical point) at the centre of a black hole. Crothers say that this implies an infinite mass. But he said once that mathematical points don't exist. Yet the infinitely dense point-mass is a mathematical point and only appears in our mathematical model, so it have no physical meaning, i.e, it doesn't exist, it just appears in the equations. Also, Crothers seems to not be aware of Quantum Mechanics and modern quantum theories such as Loop Quantum Gravity [3] or String Theory [4], who get rid out of singularities.
That's the second point.
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We now proved that infinite mass doesn't violate neither Special Relativity nor General Relativity and that singularities are just mathematical points that have no basis whatsoever in reality. Thus, Stephen Crothers claim that black hole theory violates Einstein's theory is wrong.




[1] About Ric = 0 - Stephen Crothers
[2] Igor Ivanov's answer to a relativistic mass question.
[3] Loop Quantum Gravity radicates Singularities.
[4] String theory and Singularities.