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From my very rudimentary understanding of neutron stars taken from the abstract to "Elasticity of Nuclear Pasta", nuclear pasta is the strongest substance, hence the strongest part of a neutron star.

Our results show that nuclear pasta may be the strongest known material, perhaps with a shear modulus of $10^{30}$ ergs/cm³ and a breaking strain greater than 0.1.

It seems like unbelievable pressure can only increase the closer to the core of the star. With all of the particles condensed, wouldn't that– the core– be the strongest part? Not the pasta?

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    $\begingroup$ I suspect something like journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.132701 "Our results show that nuclear pasta may be the strongest known material, perhaps with a shear modulus of 10^30 ergs/cm³ and a breaking strain greater than 0.1." $\endgroup$
    – James K
    Sep 21 at 19:40
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    $\begingroup$ @JamesK Yeah, I got it from the abstract. $\endgroup$
    – Ben A.
    Sep 21 at 19:44
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    $\begingroup$ Okay I've edited based on hyour comment. $\endgroup$
    – James K
    Sep 21 at 19:53

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The paper is discussing "strength" in terms of the shear modulus, which is the resistance of a material to shearing forces, not its resistance to compression. A shear modulus of $10^{30}$ erg/cm$^2$ is about 25 orders of magnitude larger than that of steel.

The deep interior of a neutron star, interior to any nuclear pasta phase, is a fluid. A fluid does not have a shear modulus. Instead it has a bulk modulus, which is a small multiple of the gas pressure, and measures the resistance of the material to compression.

The gas pressure does indeed increase towards the centre of the neutron star. In conclusion, the fluid at the centre is less compressible than nuclear pasta, but nuclear pasta is "stronger" in terms of resistance to shearing forces.

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