because the mass of Jupiter is not sufficient to cause collapse into a black hole by itself the only way that we could possibly make this event occur is by means of a sort of burst compression activity. The condition upon which we will have made a successful collapse is that we keep a mass inside some spherical volume with the constraints that we keep the mass there long enough for light to traverse a diameter of the volume (so that the gravitational field definitely has enough time to set up) and also that the amount of mass inside the volume exceeds some threshold. The Schwartzchild radius is r = 2*G*m/c2 if you translate that into a necessary density based on the available mass you get m/V = 3 * c6 / (32 * Pi * G3 * m 2 ) You will notice that the necessary density goes down with increasing mass. Unfortunately c6 * G-3 is a really freaking big number about 1081 fortunately mass is in there as an inverse square so when you get to really high masses the required density is actually pretty low. If you happen to have a mass of about 1038 Kg involved then the required density is about the density of water.
If you read previous posts on my plan to collapse Jupiter into a black hole then you will know that I was thinking of a strategy that used several million megatons of nuclear bombs to drive a shockwave into the core of Jupiter in the hopes that I could drive the density of the region high enough to cause complete gravitational collapse. Recently I made a visit to INL (Idaho National Labs) and talked to someone there about the possibility of bubble fusion. The concept of bubble fusion is that you release bubbles of deuterium and tritium into some medium and have freaking loud sound waves resonating in the liquid. When the sound waves hit the bubbles of gas they violently compress it causing huge temperatures and pressures which theoretically can be enough to cause fusion inside the bubbles. I don't know if you could really get a positive energy yield out of doing fusion reactions this way. The guy I talked to seemed to think that a positive energy yield was completely out of the question. I genuinely think you could probably get a positive energy yield from a bubble fusion sort of device maybe nucleate the bubbles in a blanket of molten lithium you could get good shielding and breed tritium that way.
Bubble fusion is not the point though, the point is that resonance is cool and that maybe a single burst is not the most efficient way of going about doing it. Although producing many millions of megaton nuclear bombs is something that is theoretically within the technical grasp of humanity I would say that is still somewhat of a brute force strategy. What would otherwise have had to be done all at once in a huge burst of energy could instead be done over a period of years of carefully tuned resonances. Ideally it would be nice to be able to get a radial resonance going inside of Jupiter so that the pressure waves go directly down into the core and then bounce off each other creating amazingly high pressures at Jupiter's core while leaving the devices actually causing the sound waves in relatively safe and low pressure environments near the surface of the planet. How exactly these sound waves are to be produced is a matter for a future post. Also I would be willing to bet that the simplest radial standing wave pattern resonance is not stable and one would have to design something with a little more robustness.