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Expansion of non‐spherical relativistic blast waves is considered in the Kompaneets (the thin‐shell) approximation. We find that relativistic motion effectively ‘freezes out’ the lateral dynamics of the shock front: only extremely strongly collimated shocks, with opening angles Δθ≤ 1/Γ 2 , show appreciable modification of profiles due to sideways expansion. For less collimated profiles, the propagation is nearly ballistic; the sideways expansion of relativistic shocks becomes important only when they become mildly relativistic. Even though the post‐shock pressure is equilibrated downstream on the sound crossing time‐scale, this does not mean that the shape of the shock changes on the post‐shock sound crossing time‐scale.

On the sideways expansion of relativistic non‐spherical shocks and gamma‐ray burst afterglows