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(Abridged) We discuss a Gamma-ray burst (GRB) fireball with an additionalenergy injection, either in the form of a Poynting-flux-dominated outflow or akinetic-energy-dominated matter shell injected after the burst. A totalinjection energy comparable to that of the impulsive energy in the initialfireball is required to make a detectable signature in the afterglowlightcurves. For the case of a Poynting-flux-dominated injection, this leads toa gradual achromatic bump feature. For the case when the injection iskinetic-energy-dominated, the collision between the rear (injected) and theforward shell mild if the relative velocity between the colliding shells doesnot exceed a critical value defined by their energy ratio. Otherwise, theinjection is violent, and an additional pair of shocks will form at thediscontinuity between two colliding shells, so that there are altogether threeshock-heated regions from which the emission contributes to the finallightcurves. We describe the shell-merging process in detail and presentbroadband lightcurves with the injection signatures. A violent collisionresults in very complicated features, which differs from the gradual bumpsignature found in the Poynting-flux or mild matter injection cases. In all thecases, the energetics of the fireball as well as the absolute afterglow fluxlevel after the injection are boosted after the injection. Identifying thedifferent injection signatures from future early afterglow observations mayprovide diagnostics about the nature of the fireball and of the central engine.Comment: emulateapj style, 12 pages, 8 figures, final version accepted for  publication in Ap

Gamma‐Ray Bursts with Continuous Energy Injection and Their Afterglow Signature