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We show that an extragalactic jet with a velocity shear gives rise to Fermilike acceleration process for photons scattering withing the shear layers ofthe jet. Such photons then gain energy to produce a high energy power law.These power law spectra at high energies are frequently observed in severalextragalactic objects such as Gamma Ray Bursts (GRBs). We implement the modelon GRBs to show that the obtained range of the photon indices are well withintheir observed values. The analytic results are confirmed with numericalsimulations following Monte Carlo approach.

Photon scattering in a relativistic outflow having velocity shear: a novel mechanism of generation for high energy power-law spectra