We study the dynamics of relativistic electromagnetic explosions as a possible mechanism for the production of Gamma-Ray Bursts. We propose that a rotating relativistic stellar-mass progenitor loses much of its spin energy in the form of an electromagnetically-dominated outflow. After the flow becomes optically thin, it forms a relativistically expanding, non-spherically symmetric magnetic bubble - a cold fireball. We analyze the structure and dynamics of such a cavity in the force-free approximation. During relativistic expansion, most of the magnetic energy in the bubble is concentrated in a thin shell near its surface (contact discontinuity). We suggest that either the polar current or the shell currents become unstable to electromagnetic instabilities at a radius $sim10^{16}$ cm. This leads to acceleration of pairs and causes the $gamma$-ray emission. At a radius $sim10^{17}$ cm, the momentum contained in the electromagnetic shell will have been largely transferred to the surrounding blast wave propagating into the circumstellar medium. Particles accelerated at the fluid shock may combine with electromagnetic field from the electromagnetic shell to produce the afterglow emission.
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