The detection of optical rebrightenings and X-ray plateaus in the afterglows of gamma-ray bursts (GRBs) challenges the generic external shock model. Recently, we have developed a numerical method to calculate the dynamics of the system consisting of a forward shock and a reverse shock. Here, we briefly review the applications of this method in the afterglow theory. By relating these diverse features to the central engines of GRBs, we find that the steep optical rebrightenings would be caused by the fall-back accretion of black holes, while the shallow optical rebrightenings are the consequence of the injection of the electron-positron-pair wind from the central magnetar. These studies provide useful ways to probe the characteristics of GRB central engines.
Electron–positron pair production by linearly polarized photon in the nuclear field