Time Delay between Neutrinos and Gamma-Rays in Short Gamma-Ray Bursts

In this Letter we make an estimate of the time delay between signals, recorded at detectors on Earth, of neutrinos and photons originated in a short gamma-ray burst. We describe the geometry and dynamics of the system according to the Fireshell model. The delay in the photon's arrival time is produced because the system is originally opaque to radiation; thus, the photons remain trapped and thermalize until the transparency condition is reached. We calculate the time interval between neutrino emission and photon emission in the black hole frame and transform it to the observer frame using Lorentz transformations. We obtain a difference in the arrival time at Earth of ${\rm{\Delta }}{t}_{\mathrm{Earth}}\approx 854.57\,{\rm{s}}$.