This is now a long-disused thread. However, maybe somebody will visit again, and respond.
The original question was, as the rest of this thread makes clear, obviously Science-Fiction in nature. Most of the responses addressed why Neutronium Armor couldn't be made/used/exist, (at least, with our current understanding of the Universe). They did not actually address the question itself, which starts with the presumption that such armor could somehow exist.
Since I can envision ways in which such armor could exist (although I can't tell you how craft it), I think most of you have completely dodged a legitimate question.
Examples of Neutronium Armor that could probably maintain existential stability include:
- A neutron star - Interpose a neutron star between a target and an attack, and you ipso facto have neutronium armor. What would be the characteristics and utility of such armor in this case? For example, I would suspect it would not provide very effective armor against the gamma-ray blast of a quasar because of gravitational lensing. If you were close-enough to the neutron star that the lensing effect didn't "erase" the neutron-star's shadow, they you were probably "too close" to the neutron star in the various ways already presented in this thread. However, I haven't even attempted to run the math, so I might be way off on how much the gravitational lensing effect would bend the paths of the cosmic rays.
- Thin, hollow neutronium shell - IIRC, the theoretical net gravitational "pull" inside a massive but thin hollow sphere (regardless of density) is zero, within the interior. Obviously, this mathematically assumes "thin" equals "zero thickness", which can't actually happen. However, what happens if "thin" equals "a minuscule percentage of the spherical radius"? Again, I haven't run the math (and it's been 3 decades since I used any calculus), but I suspect that there would be a fair-sized spherical interior region that exhibited tolerable levels of gravitational flux. Basically, we are most-worried about tidal effects across the largest chord of the object(s) we are attempting to shield with the armor. If this assumption is correct, then obviously there is some size of hollow sphere for which the net gravitational effect at the sphere's surface is sufficient to maintain the neutronium state. Granted, this may require more matter than exists in the known universe, but still it *could happen* ;-)
- Gigantic Hollow Tube - Like the already-referenced Star-Trek doomsday machine. I'm not at all certain of the gravitational-flux physics of a hollow neutronium cylinder, spinning at a high-enough rate around its axis to maintain a cylindrical shape. It's mere existence would probably constitute a pretty good doomsday machine, even without some postulated star-annihilating weapon. However, postulating another sci-fi favorite - gravitic technology - might allow the maintenance of a "safe" region along the axis of the cylinder. At least, away from the ends, anyway. Again, what would the armor-characteristics of an enormous, rapidly-spinning cylinder of neutronium be?
Science Fiction, in it's "purest" sense, involves postulating some as-yet-impossible effect, and analyzing the implications on the rest of the otherwise-held-constant universe, both in terms of societal impact (the most popular expression of sci-fi), and in terms of pure physics. I feel that, in this latter expression, this question about neutronium armor is, in fact, a legitimate physics question. If some technique
did exist for crafting neutronium armor, what are the resulting physical-science implications?
For example, the much-postulated sci-fi technology of "gravitics" - the ability to artificially manipulate the gravitational field in a given volume of space - would probably lend itself quite well to the collection, machining, and maintenance of neutronium. On the other hand, while anti-gravity, tractor-beams, and pressor-beams are obvious implied applications of gravitics, I think you could make some pretty dandy force-fields, too. A "black-hole level" repulsive gradient in a sphere around a "constant 1-gravity" spaceship interior would probably be a much better armor than "mere" neutronium. It might also incidentally provide a means of faster-than-light travel, since the ship-interior would be totally divorced from the rest of the universe - and thus, it's position might be an imaginary number only, which can be adjusted without pesky relativistic effects - until the force-field was deconstructed.
Similarly, some sort of "stasis" time-stop technology would allow the maintenance-of-state of neutronium (or anything else). Of course, a true stasis field would also probably be a better armor than "mere" neutronium, since there can be no energy-propogation in a time-stopped environment.