In this paper link.aps.org/doi/10.1103/PhysRevD.50.3666 the authors discuss the gravitational shock wave metric produced by massless particle:
and they find there is a jump of coordinate for geodesics:
$\Delta v=\text{const. ln}\frac{\rho^2}{\text{const.}}$ $\qquad$ (2a)
There are two singular behaviors for this formula: the first one is the logarithmic singularity and the authors comment that at extremely high energy scale interaction due to this shock wave will dominate other quantum interaction for the latter will be postponed by an infinite time shift. We can argue that at highE GR should be corrected and this will be solved.
The second is more confusing: when $\rho$ is sufficiently large, there is a infrared divergence due to the logarithm. We can argue that only the difference of $\Delta v$ is observable for local observers, but once the constants are fixed, the global geometry is detemined and you can imagine a picture that a photon coming from the past (like CMB) shocks the whole universe: this is really a nonlocal phenomenon caused by a local particle.
So my question is that what is the correct physical interpretation of these kinds of shock wave solutions.
ps: the orginal work of flat st. shock wave is due to Aichelburg and Sexl but I don't have that in hand, and for the shock wave in general background st. 9408169v3 is a good reference.


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