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We find self-similar solutions to describe the interaction of sphericallysymmetric ejecta expanding at relativistic speeds with an ambient medium havinga power law density distribution. Using this solution, the time evolution ofthe Lorentz factor of the outer shock is derived as a function of the explosionenergy, the mass of the ejecta, and parameters for the ambient medium. Thesesolutions are an ultra-relativistic version of the solutions for thecircumstellar interaction of supernova ejecta obtained by Chevalier andextensions of the relativistic blast wave solutions of Blandford & Mckee.Comment: 12 pages, 1 figure, accepted for publication in Ap

Self‐similar Solutions for the Interaction of Relativistic Ejecta with an Ambient Medium