Formulation for the Relativistic Blast Waves and GRB Afterglows

We present a detailed description of the blast-wave modeling technique for a very general class of GRB explosions. Providing a simple method of evaluating the blast energy, we demonstrate that a common approximation of pressure balance for the blast wave violates the energy-conservation law significantly for adiabatic blast waves. We show that the energy-violation problem is successfully resolved by the "mechanical model" that we developed. GRB afterglow lightcurves that are produced by the forward and reverse shock waves of the blast wave are presented.