JackDole wrote:Source of the post Why is this differentiation made, rotating and non-rotating neutron stars? There are almost certainly no non-rotating neutron stars in the universe!
Well, you see, physicists have an awful habit of oversimplifying things.
(No, in seriousness it's a very fine question.) The real answer is that in physics we do prefer simplifying things first. We construct simple models first to get some insight, and then build up to a more realistic or general case and see how that modifies things. Knowing the mass limit for simple non-spinning neutron star serves as a benchmark and from there we can look at what happens if we introduce spin or other parameters.
Likewise all black holes in nature certainly spin (most quite rapidly!), but the non-spinning Schwarzschild black hole was the first to be mathematically understood (1916, just a year after Einstein developed general relativity). The equations for the spinning Kerr black hole were not solved until 1963. So while the spinning black hole solution is more realistic, it is also a great deal more complicated!
Someone doing serious modelling of astrophysical black holes will of course use the Kerr solution, but students learning general relativity will almost always be introduced to the Schwarzschild solution first, because it provides the most insight to black holes and general relativistic effects for the least amount of mathematical difficulty. It also turns out to be an incredibly useful approximation for the gravitational field of stars and planets. The Kerr solution can come in later, when one wants to understand how the rotation modifies the behavior.
A non-spinning black hole can be made by colliding exactly counter-rotating black holes (possible but unlikely), but another way spin can be reduced is by the Penrose Process. In principle there is nothing that prevents an advanced civilization from harvesting enormous amounts of energy from spinning black holes, and after all that has been harvested they would be left with a "dead" non-spinning black hole.
The other extreme for black hole spin is to have it spin as quickly as possible. Very weird and interesting things happen in that solution, though it probably never happens. Nature gets "almost there", with the upper limit of about 99.8% of the fastest possible rotation speed.