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Forward shocks caused by the interaction between a relativistic blast waveand the circum-burst medium are thought to be responsible for the afterglowemission in Gamma-Ray Bursts (GRBs). We consider the hydrodynamics of aspherical relativistic blast wave expanding into the surrounding medium and wegeneralize the standard theory in order to account for several effects that aregenerally ignored. In particular, we consider the role of adiabatic andradiative losses on the hydrodynamical evolution of the shock, under theassumption that the cooling losses are fast. Our model can describe adiabatic,fully radiative and semi-radiative blast waves, and can describe the effects ofa time-varying radiative efficiency. The equations we present are valid forarbitrary density profiles, and also for a circum-burst medium enriched withelectron-positron pairs. The presence of pairs enhances the fraction of shockenergy gained by the leptons, thus increasing the importance of radiativelosses. Our model allows to study whether the high-energy (>0.1 GeV) emissionin GRBs may originate from afterglow radiation. In particular, it is suitableto test whether the fast decay of the high-energy light curve observed inseveral Fermi LAT GRBs can be ascribed to an initial radiative phase, followedby the standard adiabatic evolution.

Afterglow emission in Gamma-Ray Bursts: I. Pair-enriched ambient medium and radiative blast waves