Gravitational shock waves and vacuum fluctuations

@article{Hortasu1998GravitationalSW,
  title={Gravitational shock waves and vacuum fluctuations},
  author={M. Hortaçsu and K. Ulker},
  journal={Classical and Quantum Gravity},
  year={1998},
  volume={15},
  pages={1415-1420}
}
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. 
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