# Electric field in a gravitational shockwave geometry?

1. Jul 12, 2015

### Physics Monkey

Hi all,

I'm interested in the behavior of electric fields in a gravitational shockwave geometry. I'm specifically thinking about gravitational shockwaves due to null shells as discussed, for example, in Dray-'tHooft http://www.sciencedirect.com/science/article/pii/0550321385905255 (available here as well http://dspace.library.uu.nl/handle/1874/4758).

The basic feature of these shockwave spacetimes is that the shockwave produces a shift in one the null coordinates as the shockwave is crossed. For example, if the shockwave is given by $u=0$ then across the shockwave $v \rightarrow v + \delta v$. See Fig. 1 in the Dray-'tHooft paper.

One can also find such solutions in systems with electric charge, e.g. a charged black hole (e.g. http://arxiv.org/abs/hep-th/9408169).

My questions are:

1. What does an electric field crossing such a shockwave "look like"? Is it also "carried along" the shockwave for a while? Here I'm trying to get a sense of the physics, e.g. if the horizon in Fig. 1 had one unit of charge one it (+1 on left horizon, -1 on right, no net charge), what would the field lines look like after the shockwave?

2. Is anyone aware of a treatment of boundary conditions of electric fields (or other types of matter) across such a shockwave? 9408169 makes no mention of any special boundary conditions as far as I can tell. The assumption seems to be that nothing singular happens except in the metric and everything else is glued smoothly.

Thanks!

2. Jul 17, 2015