Do black holes exist

As black holes are formed by gravitational collapse, a vast amount of heat is generated, and the star temperature may reach 1012 K. This will oppose collapse, until it has been shed, and in losing energy the star must also lose mass. Since the Schwarzschild radius rsub(s) is proportional to mass, this also decreases; as the radius of the star decreases so does rsub(s), and the former never catches up with the latter. So how does a black hole ever form. (Auth.)