Neutrino self-energy and pair creation in neutron stars

Massless neutrino exchange leads to a new long-range force between matter. Recently, it was claimed both that the potential energy due to this interaction i) dominates the total energy of neutron stars and ii) that it is zero. We recalculate the energy of a neutrino propagating in a classical, uniform background of neutrons and find a negligible, but non-zero contribution to the total energy of neutron stars. We estimate the neutrino pair creation rate of a neutron star caused by a density gradient of the background neutrons but found it too small to be observable.