Early stages of relativistic fireball expansion

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Abstract
The expansion of a relativistic fireball is investigated analytically in the frame of relativistic hydrodynamics with an ultrarelativistic equation of state ɛ=3P. Equations of spherical flow with Lorentz factors γ≫1 are reduced to a simple form, and we present their general solution. We also get a particular solution, describing a thin spherical shell moving with ultrarelativistic speed—the leading part of a relativistic fireball. A self-similar solution for the central part of the fireball is matched with the outer shell solution, thus giving the general picture of expansion, which is in good agreement with numerical results. The obtained solutions are related to early stages of fireball expansion, appearing in γ-ray bursts of cosmological origin and within multiple production of particles.