Gamma Ray Bursts, The Principle of Relative Locality and Connection Normal Coordinates

TL;DR

This paper investigates the energy-dependent speed of light using gamma ray burst data within the framework of relative locality, demonstrating coordinate independence and torsion invariance in the predicted time delays.

Contribution

It generalizes previous calculations of gamma ray burst time delays in relative locality, confirming coordinate independence and torsion invariance of the results.

Findings

Time delay calculations are coordinate independent.

Results do not depend on torsion presence.

Generalized to broader coordinate systems.

Abstract

The launch of the Fermi telescope in 2008 opened up the possibility of measuring the energy dependence of the speed of light by considering the time delay in the arrival of gamma ray bursts emitted simultaneously from very distant sources.The expected time delay between the arrival of gamma rays of significantly different energies as predicted by the framework of relative locality has already been calculated in Riemann normal coordinates. In the following, we calculate the time delay in more generality and then specialize to the connection normal coordinate system as a check that the results are coordinate independent. We also show that this result does not depend on the presence of torsion.