$quadratic$ in $\lambda_P$.

Nevertheless, a rough estimate of the deviation angle $\theta$ of an electron by a compact object of mass $M$ and radius $R$ spinning at angular velocity $\omega$ gives, using , $$\theta \cong \frac{M_S}{m\gamma R^2} \cong \frac{e \lambda_P^2 M \omega}{m \gamma R},$$ with $m$ the electron mass and $\gamma = (1-v^2)^{-1/2}$. Choosing, as above, $M \simeq 10^{56} \,GeV$, $R \simeq 10^{-1}\, km$ and $\omega = 10^2 s^{-1}$ the deviation would be only $\theta \cong 10^{-34}$ for electrons of energy $1\, TeV$, which would reach us with a delay, with respect to photons, of a few hours if the source is $10^9$ light years distant. The delay for protons of $10^3 \,TeV$ (still considered to be lower than the GKW limit) would be the same, but the deviation would be $10^3$ times smaller. Of course the deviation would be more important for softer electrons, which however would reach the Earth when nobody is there any longer.

Moreover, a “less favorable” aspect is that electrons are considerably influenced by the much stronger galactic magnetic field, of which a precise knowledge would be needed, together with a nearly exact location in the sky of the sources of electromagnetic radiation and of 