At a distance, is there any difference between the gravitational fields of two bodies of identical mass but different densities?
As an extreme example, take a planet orbiting at a distance of say 20 AU from a star of say 50 solar masses. Such a star undergoing core collapse can become a black hole without any supernova explosion. What would happen to the planet in orbit around this star? There would certainly be an impact – “day” would become permanent “night”, as the light and warmth of the star would disappear. But the mass that the planet was gravitationally bound to is still there in the same location, the only difference is that it’s now compressed into a single point. Does this change in density make any difference to the gravitational field?
NB: I wanted to use the extreme example of direct core collapse to a black hole, but I realise "density" isn't the right word when referring to a singularity, so if that affects the potential answer, also consider the comparison between two solar systems each with a planet of identical mass orbiting at identical distance around a star of identical mass, but one star is main sequence and the other is a neutron star.