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Neutron stars can be destroyed by black holes at their center accreting material and eventually swallowing the entire star. Here we note that the accretion model adopted in the literature, based on Bondi accretion or variations thereof, is inadequate for small black holes -- black holes whose Schwarzschild radius is comparable to, or smaller than, the neutrons de Broglie wavelength. In this case, quantum mechanical aspects of the accretion process cannot be neglected, and give rise to a completely different accretion rate. We show that for the case of black holes seeded by the collapse of bosonic dark matter, this is the case for electroweak-scale dark matter particles. In the case of fermionic dark matter, typically the black holes that would form at the center of a neutron star are more massive, unless the dark matter particle mass is very large, larger than about 10$^{10}$ GeV. We calculate the lifetime of neutron stars harboring a small black hole, and find that black holes lighter than $sim 10^{11}$ kg quickly evaporate, leaving no trace. More massive black holes destroy neutron stars via quantum accretion on time-scales much shorter than the age of observed neutron stars.
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We investigate the nuclear pasta phases in neutron star crusts by conducting a large number of three-dimensional Hartree-Fock+BCS calculations at densities leading to the crust-core transition. We survey the shape parameter space of pasta at constant pressure. Spaghetti, waffles, lasagna, bi-continuous phases and cylindrical holes occupy local minima in the resulting Gibbs energy surfaces. The bi-continuous phase, in which both the neutron gas and nuclear matter extend continuously in all dimensions and therefore protons are delocalized, appears over a large range of depths. Our results support the idea that nuclear pasta is a glassy system. Multiple pasta configurations coexist in a given layer of the crust. At a characteristic temperature, of order $10^8$-$10^9$K, different phases become frozen into domains whose sizes we estimate to be 1-50 times the lattice spacing and over which the local density and electron fraction can vary. Above this temperature, there is very little long-range order and matter is an amorphous solid. Electron scattering off domain boundaries may contribute to the disorder resistivity of the pasta phases. Annealing of the domains may occur during cooling; repopulating of local minima during crustal heating might lead to temperature dependent transport properties in the deep layers of the crust. We identify 4 distinct regions: (1) nuclear pasta first appears as a local minima, but spherical nuclei are the ground state; (2) nuclear pasta become the absolute minimum, but spherical nuclei are still a local minimum (3) only nuclear pasta appears in local minima, and protons are still localized in at least one dimension (4) only pasta appears, and protons are delocalized. The whole pasta region can occupy up to 70% of the crust by mass and 40% by thickness, and the layer in which protons are delocalized could occupy 45% of the crust mass and 25% of its thickness.
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