Hypothetically, if neutrinos lost their energy in the expanding universe, slowed down, and collapsed in a vast and otherwise empty region under their own gravity, they might form a large object usually referred to as "neutrino star". The Pauli exclusion principle would not allow neutrinos to collapse all the way to the center, so they would form a surface that with enough gravity might be liquid or solid.
My question is on the Pauli exclusion principle. Would it allow me to stand on the solid surface or sail in a boat on a liquid surface of a neutrino star? Or would I just fall through all the way to the center, because I am not made of neutrinos and the Pauli exclusion principle for neutrinos does not apply to me? If so, what would be my experience? Would I feel the presence of the dense neutrino matter or would I perceive this star as a gravitational trap in a seemingly empty space?
Answer
Far out, man!
This is not a complete answer, but is too long for a comment.
For white dwarfs and neutron stars, we have pretty limited ranges of possible masses. Too light, and gravitational collapse produces a Jupiter rather than an evolutionary track ending in a degenerate star. Too heavy, and you surpass the Chandrasekhar or Tolman-Oppenheimer-Volkoff limit.
It seems like things are much more wide open for a neutrino star. Because there is no strong or EM interaction, I don't see why there would be any lower mass limit. The upper limit goes like $(hc/G)^{3/2}m^{-2}$, where $m$ here is the mass of the neutrino. Since the mass of a neutrino is about $10^7$ times smaller than that of an electron, the Chandrasekhar limit for a neutrino star is about $10^{14}$ times greater than that of a white dwarf. In other words, one of these objects can have a mass ranging from the microscopic to greater than that of a galaxy cluster.
So it's not obvious to me whether you can say much about the general case of a material object passing through one of these things. When we talk about neutrinos interacting with baryonic matter, we're used to talking about neutrino fluxes that are on a certain order of magnitude, and neutrino energies on a certain order of magnitude. Maybe someone with better particle theory chops than mine could tell us whether there is anything you could say that would apply over this huge range of parameters.
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