We investigate the origin of the prompt and delayed emission observed in the short GRB 090510 .
We use the broad-band data to test whether the most popular theoretical models for gamma-ray burst emission can accommodate the observations for this burst .
We first attempt to explain the soft-to-hard spectral evolution associated with the delayed onset of a GeV tail with the hypothesis that the prompt burst and the high energy tail both originate from a single process , namely synchrotron emission from internal shocks .
Considerations on the compactness of the source imply that the high-energy tail should be produced in a late-emitted shell , characterized by a Lorentz factor greater than the one generating the prompt burst .
However , in this hypothesis , the predicted evolution of the synchrotron peak frequency does not agree with the observed soft-to-hard evolution .
Given the difficulties of a single-mechanism hypothesis , we test two alternative double-component scenarios .
In the first , the prompt burst is explained as synchrotron radiation from internal shocks , and the high energy emission ( up to about 1 s following the trigger ) as internal shock synchrotron-self-Compton .
In the second scenario , in view of its long duration ( \sim 100 s ) , the high energy tail is decoupled from the prompt burst and has an external shock origin .
In this case , we show that a reasonable choice of parameters does indeed exist to accommodate the optical-to-GeV data , provided the Lorentz factor of the shocked shell is sufficiently high .
Finally , we attempt to explain the chromatic break observed around \sim 10 ^ { 3 } s with a structured jet model .
We find that this might be a viable explanation , and that it lowers the high value of the burst energy derived assuming isotropy , \sim 10 ^ { 53 } erg , below \sim 10 ^ { 49 } erg , more compatible with the energetics from a binary merger progenitor .