*Lukas Weih, ITP, Goethe Universität Frankfurt*

The stability properties of rotating relativistic stars against prompt gravitational collapse to a black hole are rather well understood for uniformly rotating models. This is not the case for differentially rotating neutron stars, which are expected to be produced in catastrophic events such as the merger of binary system of neutron stars or the collapse of a massive stellar core. In my Master thesis, which I present in this talk, I combine sequences of differentially rotating models with their dynamical evolution and show in this way that a sufficient stability criterion for differentially rotating neutron stars exists similar to

the one of their uniformly rotating counterparts. Namely: along a sequence of constant angular momentum, a dynamical instability sets in for central rest-mass densities slightly below the one of the equilibrium solution at the turning point. In addition, it is shown that “quasi-universal” relations can be found when calculating the turning-point mass. In turn, this allows to compute the maximum mass allowed by differential rotation in terms of the maximum mass of the nonrotating configuration.