I made a mistake. I meant that the situation of having one lump of clay (which isn't a black hole) at rest in a frame is different than having two lumps of clay approaching each other.Zanket said:I don’t see how it’s two different frames in the “case I’ve just explained.” It seems to me that it’s all happening in my frame. Things can move in my frame right?
It takes more than energy to create a black hole. There is enough mass in my body to create a black hole. All that needs to be done to create a black hole is to have all my matter within a much smaller region of space.Say I’m floating in deep space, watching a light-year-in-diameter sphere of space. Within that sphere are the two lumps of clay (let’s say boxcar-sized) approaching each other. They collide in the middle of the sphere, releasing enough heat energy to create a black hole with an event horizon that encloses the sphere. Didn’t I witness a black hole spontaneously form in a region of space to which no mass was added? All in one frame?
In what you've just described, that energy must be compressed into a region of space so small as to have all the matter all within the Schwarzchild radius. However the mass remained constant in the situation you just described. Because mass is a conserved quantity the total mass in the end was identical to the total mass in the beginning. You forgot that there is mass just due to the motion of the clay lumps, i.e. the fast a lump of clay, the greater its mass is.