Relativistic Shells and $\gamma$-Ray Bursts

In many models of Gamma-Ray Bursts (GRBs) relativistic shells are responsible for the overall envelope of emission. We use kinematics and symmetry to calculate the time history and spectral evolution expected from a relativistic shell including effects from intrinsic variations in the shell's intensity and spectra. We find that the decay phase of an envelope is produced by photons delayed by the shell's curvature. These delayed photons are produced by regions that are off-axis such that the spectra evolve according to a universal function (T^{-1}) regardless of intrinsic variations in the rest frame of the shell. We compare our predictions to the overall envelope of emission of GRBs. The observed spectra evolve faster. Intrinsic variations cannot make the spectra evolve that fast, which adds strength to the ``shell symmetry'' problem: models, in particular, the external shock model, that involve relativistic shells must either confine the material to narrow pencil beams, be very inefficient, or break the local spherical symmetry so that the shell acts like a parallel slab. In the case of the internal shock models involving winds (i.e., central engines), it will probably be easier to break the local spherical symmetry, but then one must postulate nearly continuous energy generation at 10^{51} erg s^{-1} lasting up to hundreds of seconds at the central site