Convective instability in proto-neutron stars

The linear hydrodynamic stability of proto-neutron stars (PNSs) is consider ed, taking into account dissipative processes such as neutrino transport an d viscosity. We obtain the general instability criteria, which differ essen tially from the well-known Ledoux criterion used in previous studies. We ap ply the criteria to evolutive models of PNSs that, in general, can be subje ct to the various known regimes such as neutron fingers and convective inst abilities. Our results indicate that the fingers instability arises in a mo re extended region of the stellar volume and lasts a longer time than expec ted.