Effects of conversions for high energy neutrinos originating from cosmological gamma-ray burst fireballs

We study neutrino conversions in the recently envisaged source of high energy ($E \geq 10^{6}$ GeV) neutrinos, that is, in the vicinity of cosmological gamma-ray burst fireballs (GRB). We consider mainly the possibility of neutrino conversions due to an interplay of neutrino transition magnetic moment, $\mu$, and the violation of equivalence principle (VEP), parameterized by $\Delta f$, in a reasonable strength of magnetic field in the vicinity of the GRB. We point out that for $\Delta f \sim 10^{-25}(\delta m^2/1 {eV}^2)$, a resonant spin-flavour precession between $\bar{\nu}_{\mu}$ and $\nu_{\tau}$ may occur in the vicinity of GRB for $\mu \sim 10^{-12} \mu_{B}$ ($\mu_{B}$ is Bohr magneton), thus enhancing the expected high energy $\nu_{\tau}$ flux from GRBs.