The onset of the GeV afterglow of GRB 090510

We study the emission of the short/hard GRB 090510 at energies > 0.1 GeV as observed by the Large Area Telescope (LAT) onboard the Fermi satellite. The GeV flux rises in time as t^2 and decays as t^-1.5 up to 200 s. The peak of the high energy flux is delayed by 0.2 s with respect to the main ~MeV pulse detected by the Fermi Gamma Burst Monitor (GBM). Its energy spectrum is consistent with F(E)=E^-1. The time behavior and the spectrum of the high energy LAT flux are strong evidences of an afterglow origin. We then interpret it as synchrotron radiation produced by the forward shock of a fireball having a bulk Lorentz factor Gamma ~ 2000. The afterglow peak time is independent of energy in the 0.1-30 GeV range and coincides with the arrival time of the highest energy photon (~ 30 GeV). Since the flux detected by the GBM and the LAT have different origins, the delay between these two components is not entirely due to possible violation of the Lorentz invariance. It is the LAT component by itself that allows to set a stringent lower limit on the quantum-gravity mass of 4.7 times the Planck mass.