# Upper limit of neutron star mass and collapse to a black hole

1. What is the exact lower limit mass of a black hole? Or to be more precise, what is the border which where a massive star turns from a neutron star to a black hole?

2. Can a neutron star with maximum possible mass turn into a black hole by just absorbing minimum possible mass (Planck mass) ?

• How would that be a superposition? It would be a neutron star, and then it would turn into a black hole. Jan 12, 2021 at 2:42
• Yes, that's why I said in "some kind of super position". I was just trying to imply a neutron star with a upper limit mass. Jan 12, 2021 at 2:45
• OK just to avoid other people getting confused, that's not how the word superposition is used in physics. Jan 12, 2021 at 2:46
• You are completely correct, just a better word didn't came up to me. Can you edit the question if you have a better way to represent the question? Jan 12, 2021 at 2:48
• Jan 12, 2021 at 14:50

1. For your more general question, in classical general relativity, there is no lower mass limit to a black hole; you may make it as large or as small as you wish. For your more precise question, the upper bound to a non-rotating neutron star is the Tolman-Oppenheimer-Volkoff limit, which is between 2.1 to 2.3 solar masses. Beyond this, the neutron star will collapse into a black hole.

2. We do not yet have a perfect quantitative understanding of the interior of a neutron star, so currently this question is unanswerable. However, assuming our neutron star is a static, spherically symmetric mass made of a perfect fluid with a density that increases outwards, then we must have $$M<\frac{4Rc^2}{9G}$$ where $$R$$ is the (areal) radius, $$c$$ is the speed of light, and $$G$$ is the gravitational constant. This is Buchdahl's theorem. So, if a neutron star obeyed the above (fairly reasonable) postulates, and was able to be brought right below the limit (which may or may not be the case), then it would be in the situation you describe; shoving in even a little bit more mass would inevitably cause collapse to a black hole.