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11

Technically, there would be minute differences due to the gravitational field generated by the mass of the spacecraft tidally deforming the neutron star leading a small response in the gravitational field of the neutron star, which in turn effects the orbit of the spacecraft. This tidal response is governed by the so called tidal Love numbers of the Neutron ...

20

If they were spinning they would be distinguishable (in principle), otherwise not. Astrophysical black holes and neutron stars are expected to spin. In the case of a neutron star that automatically means that the mass/energy distribution is not spherically symmetric and therefore that the detail of the potential outside the surface depends on the detail of ...

22

Birkhoff's theorem is very useful: in general relativity, if you are in vacuum and there is a spherically symmetric gravitational field, then it will be the Schwarzschild solution. This solution only depends on the mass, not on the size of the object. So the neutron star and the black hole will give rise to exactly the same orbits.

2

Yes it would. It is that way because the effective temperature is defined to be $(L/4\pi \sigma R^2)^{0.25}$. The radius of a neutron star is about 10 km $(1.4\times 10^{-5}R_\odot)$. They are born with surface temperatures of around $10^8$ K. The coldest white dwarfs have effective temperatures of about 3000 K. The luminosity ratio is  \frac{L_{\rm NS}}{...

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