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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!
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!