Neutron Stars are the collapsed cores of Massive SuperGiant stars after a Supernova 'explosion'. By astronomical standards, they are very small, having a diameter of around 20 - 30km or so, but with a density of atomic nuclei (hence the name). It's thought that there could be around a billion neutron stars in a single galaxy such as the Milky Way.
There are several aspects of neutron stars which are unknown, or do not correlate with theoretical calculations.
Their intense magnetic fields were first detected as Pulsars. Because the stars rotate very rapidly, and the field escapes primarily from the poles, then, if the rotation happens to be oriented towards Earth in a particular way, the magnetic field pulsates with extreme regularity.
Many details of the fields - which are believed to be the most intense in the universe - are unknown :
[…] we actually know surprisingly little about neutron star magnetic fields. In particular, most “measurements” of neutron star magnetic fields are indirect inferences, which are put in doubt both by their inconsistency with other observational evidence and with plausible theoretical models for the physics of their surroundings. Even less is known about the geometry of the magnetic field, its evolution, and its origin, so there is open space for speculation, modelling, and (hopefully) prediction of measurable effects that might test the theoretical ideas.
Source : arXiv.org Astro Physics Reisenegger, A.,Thesis.
Another 'unknown' concerns the relationship between the size of the stars and their mass. Because the 'Equations of State' (i.e. the details of pressure, volume, temperature, and internal energy etc.) are not known, and because the mass of neutrons, like protons, are largely due to relativistic effects (see) it's not possible to calculate a neutron star's size and mass with acceptable accuracy - the current margin of error is around 50%.
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