I see something strange: The kinetic energy required for a falling body to reach the Schwarzschild radius is $(\gamma-1)mc^{2}$, so with $\gamma$ tending to infinity at the Schwarzschild radius, the kinetic energy becomes infinite, and even greater beyond that, which doesn't make sense....
So, how do we know that at the Schwarzschild radius the falling speed of a free falling body from infinity is $c$? Why don't we assume instead that the falling speed tends towards $c$ without ever reaching it, and that the formation of a black hole is impossible because it would require infinite energy?"
