Sudden Shock Waves in modified gravity

We construct a generic asymptotic solution for modified gravity near a sudden singularity. This solution contains a fluid source with no equation of state and is function-counting stable, that is it has eleven independent arbitrary functions of the spatial coordinates as dictated by the Cauchy problem of the theory. We further show that near the sudden singularity the solution has a shock wave character with the same number of free functions in the Jordan and Einstein frame.