Summary: We show that the vacuum expectation value of the stress-energy tensor of a scalar particle on the background of a spherical gravitational shock wave does not give a finite expression in second-order perturbation theory, in contrast to the case seen for the impulsive wave. No infrared divergences appear at this order. This result shows that there is a qualitative difference between the shock and impulsive wave solutions which is not exhibited in first order.
From the conclusion: Here we have tried to show that two qualitative differences exist between the shock and the impulsive wave solutions proposed by the same group [Y. Nutku and R. Penrose, Twistor Newsletter 34, 9 (1992); Y. Nutku, Phys. Rev. D 44, 3164-3168 (1991)]. In the shock-wave solution the infrared divergences which way be use to tame the ultraviolet divergences to result in finite contributions to \(\langle T_{vv}\rangle\) are absent in second-order perturbation theory.