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.

Automated summary

We have proposed a general asymptotic solution for modified gravity near a sudden singularity. This solution involves a fluid source without an equation of state and possesses eleven independent arbitrary functions tied to the spatial coordinates, in accordance with the Cauchy problem of the theory. Additionally, we demonstrate that the solution exhibits a shock wave-like behavior near the sudden singularity, with the same number of free functions in both the Jordan and Einstein frame.