Energy Requirements for Compressing Matter into a Black Hole

[-Job-]

How much energy would it be necessary for me to compress my coffee mug into a black hole? Would i need less energy for an object with a fraction of the size of my coffee mug? How much energy would i need to collapse a single atom into a black hole, or is that not possible, and is a lot of matter a requirement?

 

[Danger]

With no math ability, this is just a rough guess. A coffee cup would have to be compressed to somewhere around the size of an electron to become a black hole. I don't think that you could find a set of pliers small enough.

 

[franznietzsche]

How much energy would it be necessary for me to compress my coffee mug into a black hole? Would i need less energy for an object with a fraction of the size of my coffee mug? How much energy would i need to collapse a single atom into a black hole, or is that not possible, and is a lot of matter a requirement?

A simpler way to think about it would be to think in terms of the force required, which would be enough force to overcome neutron degeneracy pressure. To apply that force from all directions, through a distance that would essentially compress the mug to a point would require a certain amount of work, a la
<br /> W = \int \vec{F} \cdot d\vec{r}<br />
That is roughly the amount of energy needed(I say roughly because I somewhat simplified the problem).

 

[pervect]

I tried to take a stab at this, but I'm not sure how to solve the problem of a relativistic particle in a box.

For all of the different realms (white dwars star matter, neutron degenerate matter), the key problem in computing the energy is that of fermions in a box.

The box here is going to be very small, G/c^2 is 7.42471382 × 10-28 m / kg
and the Schwarzschild radius is r=2(G/c^2) M.

I suppose that this isn't quite right due to the non-euclidean geometry inside the "box", but it would be a first stab.

It wasn't specified, but I would assume that we'd assume that the compression was adiabatic.