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Just a weird thought I had --

Typically, ordinary atomic matter can't withstand the conditions on the surface of a neutron star. Though heat is one obstacle, the main issue is of course the absurd pressures exerted by gravitational force.

But, what if, for whatever reason, a (thermally cold) neutron star was spun up to its mass-shedding limit? The net g-force on the equatorial cusp would by definition be zero. Tidal forces would preclude anything of macroscopic size, but the force across a single micrometer would be on the order of a few tens of g. Bacteria are known to survive uniform g-forces three orders of magnitude above this, but I'm unsure about the effect of differential forces here.

I'd also be curious about what role spin-down effects would play. Is it possible for a spinning neutron star to be non-magnetic? If not, how long would it take (order-of-magnitude) until the g-forces escalated above, say, 1 million g?

whisperinggallery
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There is a lovely science fiction book named Dragon's Egg which attempted to delve into the idea of life evolving on a neutron star. While a different scenario than the one proposed it gives a much acclaimed exposition of life in extreme conditions (albeit, still some limits on its realism).

The astronomy stack exchange has some excellent answers about mass shedding on neutron stars which is helpful especially regarding neutron decay into protons and electrons in the region of low gravity. This brings up an interesting idea of the regeneration of a star if one where to add enough rotational energy to the neutron star.

There is a realtively recent but lovely paper that explores starquakes and crack formation on rapidly spinning neutron stars which can then become gas filled from the surrounding material. This is highly speculative but starts giving an interesting set of information on the environment for the life you describe.

The hardest part is that the energy levels associated with the ejection of material are all highly relativistic (e.g. high energy). Since ordinary biological life requires relatively low energy chemical bonds in order to exist it is very difficult to see how a complex molecule associated with ordinary life such as bacteria would not be broken up into magnetic goo by the intense radiation of the escaping gas.

What is interesting about your question is that there is fairly advanced research about implications of neutrino production in changing chirality of amino acids near supernova explosions to include cases where neutron stars are formed. The Supernova Amino Acid Processing model is a fascinating journey into how life and evolutionary processes could have been influenced by steller evolution, including effects of neutrinos generated by neutron stars.

Research into how bacteria develop energy shows a strong dependence on transfer of relatively low energy electrons as compared to the relativistic electrons that might be emitted as part of the formation of gas from starquakes on the neutron star. That said Deinococcus radiodurans is an extremiphile bacteria that is resistant to ionizing radiation.

Calculations regarding the intensity of radiation near a rotating neutron star are quite involved and the energies can be shown to be highly relativistic which basically dwarf the resistance of even the most resourceful extremophiles.

That said, I haven't given an explicit calculation and sadly based on above, to give an extremely satisfying one would be very involved, however from inspection of the extent literature I would feel comfortable stating that the radiation environment would be to extreme for ordinary biological life to survive long even if gravitational forces were subdued.

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