Observability of neutron events above the Greisen-Zatsepin-Kuzmin cut-off due to violation of Lorentz invariance

The clustering of ultra high energy cosmic ray events suggests that they have originated from compact sources. One of the possible physical mechanisms by which ultra high energy nuclei reach the Earth from far away astrophysical sources (quasars or BL Lac objects) evading the Greisen-Zatsepin-Kuzmin (GZK) cut-off is by violation of Lorentz invariance. Assuming that there is violation of Lorentz invariance, we calculate the expected number of neutron events from some of the EGRET sources (including $\gamma$-ray loud BL Lac objects) which can be correlated in direction with ultra high energy cosmic ray events observed by AGASA above energy $4\times10^{19}$eV. We present in this paper what AGASA should see in future if violation of Lorentz invariance is responsible for the propagation of ultra high energy cosmic rays having energies above the GZK cut-off when there is a correlation of EGRET sources with the ultra high energy cosmic ray events.