  In a core-collapse supernova, a huge amount of energy is released in the
Kelvin-Helmholtz phase subsequent to the explosion, when the proto-neutron star
cools and deleptonizes as it loses neutrinos. Most of this energy is emitted
through neutrinos, but a fraction of it can be released through gravitational
waves. We model the evolution of a proto-neutron star in the Kelvin-Helmholtz
phase using a general relativistic numerical code, and a recently proposed
finite temperature, many-body equation of state; from this we consistently
compute the diffusion coefficients driving the evolution. To include the
many-body equation of state, we develop a new fitting formula for the high
density baryon free energy at finite temperature and intermediate proton
fraction. We estimate the emitted neutrino signal, assessing its detectability
by present terrestrial detectors, and we determine the frequencies and damping
times of the quasi-normal modes which would characterize the gravitational wave
signal emitted in this stage.
