system
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human
So, any mass which is compressed past the Schwarzschild Radius becomes a black hole, but...

does that break down when you get to very small masses? Since a massive particle is a point and has no volume, does is have no S. Radius? Is is already beyond that point in some strange quantum way?
gpt
> Since a massive particle is a point and has no volume, does is have no S. Radius?

I wouldn't call it a point, or even a particle, but just a 'quantum object' that has some behaviors that are analogous to what one intuitively thinks of as a particle, and other behaviors that are analogous to what one intuitively thinks of as a wave. To know when one can reasonably apply either analogy can be difficult without a very thorough understanding of quantum mechanics.

Your question is a good one, though. 

General Relativity is an inherently classical theory. It describes the curvature of spacetime as calculated by the energy density and flow in some region of space. Mass can be considered just as internal energy, so massive objects curve spacetime to create what we perceive as gravitational attraction. 

However, the equations of general relativity are not set up to determine the curvature of spacetime from quantum objects or fields. Instead, they only work for the classical approximation of large objects, such as stars, planets, and rocks, which have very well defined energy densities.

One can do quantum mechanics, and determine the behavior of a quantum object, such as an electron, in the presence of some spacetime curvature from a classically treated object. So one can work out what might happen to quantum objects near something like a neutron star or black hole.

What currently tested and accepted theories cannot do is answer questions like yours, which is how is spacetime curved by quantum objects? This is an important question, as all big classical objects like stars are ultimately just large collections of quantum objects.

There are many candidates for a full theory or even just a framework for a theory of how gravity is produced by electrons and other fundamental particles, ranging from string theory to semi-classical theories. The naive way of getting this all to work which was done for electromagnetism didn't work for the equations of general relativity, so this is really one of the biggest open questions there is. 

Because the gravitational curvature produced by such tiny objects such as electrons is expected to be so small, it is exceptionally difficult to get any sort of experimental signal that would allow one to determine what theories of quantum or semi-classical gravity are correct or false.