First,sorry for the clickbate(kinda).
I don't know if this will work or not but It seems worth a shot unfortunately I am stuck on the approach of proving it can't be done.....'cause ofcourse it can't be!!
so my thought process goes as follows:
we take two spheres of sterile neutrinos (best suited as they only interact via gravitational forces) of radius $a$ and mass $m$. now at infinite distance apart they have, as a system ,mass of '2m'. when we bring them closer we can see it's total energy decrease as the gravitation potential energy increases. now we assume at r distance apart they have 0 mass(as a system i.e. their gravitational potential energy overcomes their mass energy) clearly 'r>2a' to be possible and we can have a minimum condition for 'a' as swartzchild radius.
it is elementary to note that it is not possible in this case as they would turn into black hole way before we can have a small enough r(which is greater than 2a).
so what I thought was to have different types of systems I tried out an equilateral triangle all the way to an octagon and also some 3-D shapes although 'the gap'(the gap refers to the diffrence between swarzchild radius and the minimum 'a' require to get 0 mass)seems to be decrasing I can't tell if the gap would be asymptotic or not.
Can anyone please prove that it is impossible for any system to have such an 'a' such that they don't turn into black hole and have so much gravitatinal potential energy to overcome their mass energy i.e. E=mc^2
if it can, I think there can be these reasons(at their decreasing order of probability).
sterile can't be captured and then thus can't be morph into spheres.
Newtons or Einsteins equations are not so nice for the small scale.
sterile neutrinos might also interact with something other than gravitational force....or maybe not interact with gravitational force.
negative mass can be formed this way(impossible and I refuse to believe it).
regardless, I just wanted to have fun with the idea and I thought this is an interesting concept.
I would really appreciate any participation. thanks for reading!