Isolated Newtonian dust stars are unstable but can be stabilized by exterior matter (Q5947423)

So-called dust stars are theoretical objects consisting of dust in the form of an ideal fluid with internal pressure \(p=0\). The mathematical problem of the existence of solutions for Newtonian dust stars is formulated. Proof for the non-existence of such stars as isolated objects are given. Comments are made on the problem of Einsteinian rotating dust stars.