# What would a sufficiently dense sphere of uranium do first: blow up, or form a black hole?

I think it is safe to assume that humans are a long way off from having either the technology to compress a normal-sized sphere of uranium below its Schwarzschild radius, or the technology to create a sphere of uranium with a mass comparable to that of a star, so this is deep into idle-curiosity-land, but supposing that we "called into existence" a sphere of uranium whose mass and density was sufficient for both the effects of nuclear fission and gravitational collapse to be relevant,

does the sphere of uranium explode due to nuclear fission, or collapse into a black hole, first?

Of course, perhaps there is a combination of effects - maybe the sphere starts to undergo fission, but forms a black hole before any explosion can take place.

• The bomb used on Hiroshima (called "Little Boy") was a critical Uranium mass assembly device. It used on order of 64 kg of 80% U-235, so in the most naive interpretation this question is a no-brainer. – dmckee Jun 25 '13 at 20:19
• @dmckee: But it didn't create conditions comparable to those where the uranium might have formed a black hole. I feel my question is fairly clear about specifying that I am imagining a situation where gravitational collapse is a relevant effect, in addition to nuclear fission. – Zev Chonoles Jun 25 '13 at 20:22
• And you're going to get that much uranium together without it first exploding, how exactly? Whatever initial configuration you envision it will have to more through a phase where you begin to increase the density. Now it is not as easy as saying "as soon as 65 kg have the natural density it goes off" because criticality is notoriously dependent of the details of geometry, but you have to keep compacting it over orders of magnitude, so your done for long before you get any kind of collapse. – dmckee Jun 25 '13 at 20:31
• @dmckee: Well, that is why I asked that the sphere be "called into existence", in a completely non-realistic way. But in comparision, I have certainly heard famous thought experiments about, for example, the Sun instantaneously disappearing - this seems like an acceptable fiction to consider. I completely agree, that it seems realistically impossible to get enough fissile material together in any way without it blowing up first. – Zev Chonoles Jun 25 '13 at 20:39
• Which either (1) violates the conservation of energy or (2) requires a pre-existing configuration of some kind of energy satisfying the requirement to be a black hole, so it is already is a black hole. – dmckee Jun 25 '13 at 20:50

Suppose we take our sphere of uranium to have the mass of the Sun, about $2 \times 10^{33}$g, then this is $8.5 \times 10^{30}$ moles of uranium 235 or $5.1 \times 10^{54}$ atoms. Fission of $^{235}$U releases $3.2 \times 10^{-11}$J per nucleus, so the total energy released would be $1.6 \times 10^{44}$ joules. This is remarkably close to the energy released by a supernova, which is in the range $10^{44}$ to $10^{46}$J.