The onset of the GeV afterglow of GRB 090510

We study the emission of the short/hard Gamma Ray Burst 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) up till 0.2 s after the peak of the MeV pulse detected by the Fermi Gamma Burst Monitor (GBM) after which it decays as t(-1.5) up to 200 s. Its energy spectrum is consistent with F(v) proportional to v(-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 with a bulk Lorentz factor Gamma similar to 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 (similar to 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. The LAT component alone allows us to set a reliable lower limit on the quantum-gravity mass of 4.7 times the Planck mass.