I think weve already had a thread like this.
But it is possible.
Photon Polarity; If you fire 2 photons from each other so they are travelling at 2c from each other, then you polarise one, the other will become polarised instaniously.
Imagine a polarise as 1 and a non polarise as 0, we have information travelling at 2c ( i think that was the point sayo missed in the other thread)
As far as your question goes, the only information that arrives to you e.g. sun explosion, will be that at the same time it happens. Even if we know the sun has exploded, running into our houses will not create a paradox, because we cannot see the affect on us at that time.