Majoron Decay in Matter

It is well known that the matter can significantly alter the picture of neutrino oscillation \cite{W} or neutrino decay \cite{BV}. Here we show that the presence of dense matter induces also the decay of {\it massless} majoron, a Goldstone boson associated with the spontaneous lepton number violation, into a couple of neutrinos with the same (or in some cases also opposite) helicities. We calculate the rates of such matter induced majoron decays in various cases, depending on the neutrino type and the chemical content of the medium, and analyse their properties.