Avengers Infinity War depicting the construction of Thor's new weapon at a neutron star is a cute and almost scientifically plausible idea. Let's assume that Mjolnir and Stormbreaker are both made of neutronium mined from neutron stars. They are extremely heavy, which explains why no one other than Thor is able to lift them. (Thor has god-like strength.)
(How do you say "Stormbreaker" in Old Norse or Icelandic?)
The weapons need to have a few additional imaginary technologies incorporated into them:
The outer shell must be a superstrong pressure vessel, able to keep its contents in the neutronium state despite being removed from the intense gravity of the neutron star. The shell also needs to withstand the impact of the weapon hitting things.
Tangentially, assuming such superstrong materials exist, how might neutron star mining realistically work? Maybe just scoop it out; far less dramatic than the movie. Dig an actual mine into the neutron star with tunnel walls built out of the pressure-resistant material. Alternatively, could an active support structure resist pressures inside a neutron star? Both Thor and Thanos (earlier, for the Infinity Gauntlet) are durable enough to survive mining inside a neutron star.
Does the density of the neutronium differ according to depth? Maybe the more powerful weapon (Stormbreaker) is made of denser neutronium from deeper in the star, or from a more massive neutron star. Maybe so dense that the material is even more exotic than neutronium, e.g., quark matter from a quark star.
Each weapon is probably massive enough to exert significant gravitational attraction on its environment, so it would be annoyingly destructive even when not being used. It needs to have some sort of antigravity generator the cancel out the gravity its mass generates. The weapons would be paradoxical objects, having gravitational masses different from their respective inertial masses. (They keep their huge inertial masses to be potent as weapons.) Maybe the antigravity generator can be turned off briefly on impact with a target, allowing its gravity to inflict additional damage.
Which attack involved more mass: Thanos throwing a moon at Iron Man, or Thor throwing Stormbreaker at Thanos?
Superheavy superdense objects tend to sink immediately to the core of the earth, undeterred by the dirt and rock in the way, which might as well be air given how relatively not dense they are compared to neutronium. The antigravity generator therefore also needs to allow the weapons to hover, not sinking, not destroying tables they are placed on.
However, once we posit this all-powerful antigravity generator that's allowing Thor and his hammer to be moved by (say) a conventional elevator, Thor doesn't have to be very strong, just good at operating the controls of the antigravity generator.
Previously on superheroes interacting with astronomical objects: (1) (2) (3)
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