Probing the equation of state of neutron stars using neutrino oscillations

We study the phenomena of neutrino oscillations and flavour mixing by incorporating the gravitational effects through the Dirac equation in curved spacetime inside a spherically symmetric star. We show that the flavour transition probabilities of the neutrinos depend on the interior spacetime metric as they propagate out of the star. As a consequence, we show that one could distinguish between different possible equation of states of nuclear matter even for an isolated neutron star if one could determine the flavour composition of emitted neutrinos near the stellar surface.