# Time-delay between neutrinos and gamma-rays in short GRBs

## TL;DR

This paper estimates the time-delay between neutrinos and gamma-ray signals from short GRBs, considering system geometry and dynamics, and finds an approximate delay of 854.57 seconds at Earth.

## Contribution

It provides a model-based calculation of the neutrino-photon arrival time difference in short GRBs using the Fireshell model and Lorentz transformations.

## Key findings

- Estimated delay of approximately 854.57 seconds at Earth.
- Demonstrated the impact of system opacity on photon emission timing.
- Applied Lorentz transformations to relate emission and observation times.

## Abstract

In this work 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- 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 $\Delta t_{Earth} \approx 854.57$ s.