Abstract
We study the properties of dense matter in neutron stars and supernovae in the relativistic mean-field (RMF) theory with non-linear σ and ω terms. The lagrangian of the RMF theory is motivated by the recent success of the relativistic Brueckner-Hartree-Fock (RBHF) theory. The parameters in the lagrangian are determined by the properties of nuclei including unstable ones and provide the equation of state of nuclear matter similar to the one in the RBHF theory. The proton fraction in neutron-star matter is found to be large enough to allow the direct URCA process for rapid cooling of neutron stars. We calculate nuclear matter having arbitrary proton fractions at finite temperature to provide the equation of state for studies of supernova explosions. The properties of supernova matter containing abundant leptons are studied in detail and the consequences on the gravitational mass of hot neutron stars at the birth era are discussed.
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