black holes. (they are reoccuring explosions)
NO.Material falling into a black hole heats up to the point where it emits X-rays, and can cause large explosions en-masse, but a blackhole is
NOT, in any sense of the word, recurring explosions.
How the hell would you "disrupt" that balance on a sun? 
The whole human nuclear arsenal combined is insignificant comapred to one solar flare. 
Hell you could hurl Earth itself into the Sun and that still wouldn't make it go nova... 
We're talking energy levels and forces so mindblogingly huge that you can't practicly comprehend them....
Geez, i'm not talking about blowing up a star per say. I mentioned the way you could do this is by removing mass from the sun. I also mentioned in many binary star systems that this alraedy happens. One star with it's gravity will start pulling mass from the other star, and by removing mass from a star, it'll eventually go critical after a certain amount of time where it starts blasting out some of it's mass in a huge cosmological event because quite easily the contracting/expanding balance stars have would have easily been disrupted.
Now the gtva should build a huge ass vacuum cleaner in space or subspace vortex that can be held open.
We're talking some kind of weird ass subspace weapon that defies the laws of physics. It has been shown in simulations that it is possible, on large enough scales, to destabilize a star. We have no idea what the heck the shivans are capable of doing, but judging from their insane technological supriority and seemingly limitless supply of resources, i wouldn't put it past them to make a star go supernova.
It is, however, completely and totally absurd that something could ever survive a supernova (and yes, they have discovered Hypernova, which are apparently over 200 times more powerful then supernova and are speculated to be caused by collapsing supergiants). For that matter, the remnants of a star that small (Capella appears to be a medium-range star similar to our own sun) would be rather insubstantial and nowhere near as thick as the nebulas normally seen in the game.