C. Relativistic Beaming and the Patchy Shell Model
The radiation from a relativistic source is beamed with a typical beaming angle 1 / . This implies that if the source that is expanding radially with an ultra-relativistic speed a given observer "sees" radiation only from a region that is within -1 from its line of sight to the source. If the radius of the emitting region is R the observer will see radiation from a region of size R / . Since is extremely large during the GRB we observe emission only from a small fraction of the emitting shell. It is possible, and even likely, that the conditions within the small region that we observe will be different from the average ones across the shell. This means that the conditions that we infer won't reflect the true average conditions within this particular GRB.
An interesting point related to the internal shocks (discussed later) model in this context is the following. According to the internal shocks model individual pulses are obtained by collisions between individual shells. Here the inhomogeneity of individual shells could be wiped out when the contributions of different hot spots from different shells is added. Alternatively the "inner engine" may produce a consistent angular pattern in which the hot spot is in the same position in all shells and in this case averaging won't lead to a cancellation of the patchy shell structure.
Within the internal-external model the GRB is produced by internal shocks in which only the relative motion within the flow is dissipated. The bulk Lorentz factor remains unchanged. During the afterglow the shell is slowed down by external shocks. As the Lorentz factor decreases with time (see Eq. 78) we observe a larger and larger fraction of the emitting region until -1, where is the angular size of the whole emitting region - the GRB jet, see Section VIIH. This has several inevitable implications. If the initial relativistic flow is inhomogenous on a small angular scale then different observers looking at the same GRB (from different viewing angles) will see different -rays light curves. A strong burst to one observer might look weak to another one if it is located at an angle larger than 1 / from the first. The two observers will see similar conditions later on, during the afterglow, as then they will observe the same angular regions. This has the following implications: (i) Given that the GRB population originate from some `typical' distribution we expect that fluctuation between different bursts at early time during the GRB will be larger than fluctuations observed at late times during the afterglow . A direct consequence of this behaviour is the appearance of a bias in the observations of GRBs. As we are more likely to detect stronger events we will tend to identify bursts in which a `hot spot` was pointing towards us during the GRB phase. If the original GRB shells are inhomogenous this would inevitably lead to a bias in the estimates of the GRB emission as compared to the kinetic energy during the afterglow. (ii) As the afterglow slows down we observe a larger and larger region. The angular structure would produces a variability in the light curve with a typical time scale of t, the observed time. These fluctuations will decay later as the Lorentz factor decreases and the observations are averaged over a larger viewing angle. Nakar et al.  have suggested that this is the source of the early fluctuations in the light curve of GRB 021004. Nakar and Oren  modelled this process with a numerical simulation. They find that the flucutation light curve of GRB 021004 can be nicely fitted by this model and that it also explains the correlated fluctuations in the polarization (see also ).