GRB afterglow light curves from uniform and non-uniform jets

Here we calculate the GRB afterglow light curves from a relativistic jet as seen by observers at a wide range of viewing angles from the jet axis, and the jet is uniform or non-uniform. We find that, for uniform jet the afterglow light curves for different viewing angles are somewhat different: in general, there are two breaks in the light curve, corresponding to the time $\gamma\sim (\theta_j-\theta_v)^{-1}$ and $\gamma\sim (\theta_j+\theta_v)^{-1}$ respectively. However, for non-uniform jet, the things become more complicated. For the case $\theta_v=0$, we can obtain the analytical results, for $k8/(p+4)$ there should be only one break corresponds to $\gamma\sim\theta_c^{-1}$, and this provides a possible explanation for some rapidly fading afterglows whose light curves have no breaks since the time at which $\gamma\sim\theta_c^{-1}$ is much earlier than our first observation time. For the case $\theta_v\neq 0$, our numerical results show that, the afterglow light curves are strongly affected by the values of $\theta_v$, $\theta_c$ and $k$. If the values of $\theta_v/\theta_c$ and $k$ are larger, there will be a prominent flattening in the afterglow light curve, which is quite different from the uniform jet, and after the flattening a very sharp break will be occurred at the time $\gamma\sim (\theta_v + \theta_c)^{-1}