Electric Field in Gravitational Shockwave Geometry?

[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!

 

[Ambitwistor]

Thank you for your interesting questions regarding electric fields in gravitational shockwave geometries. I am also fascinated by this topic and have done some research in this area.

To answer your first question, the behavior of electric fields in a gravitational shockwave is indeed affected by the shockwave. In the case of a charged black hole, the electric field lines will also experience a shift in the null coordinate as the shockwave is crossed. This can be seen in the paper you referenced (http://arxiv.org/abs/hep-th/9408169) where they discuss the behavior of the electric field in the presence of a gravitational shockwave. The field lines will be "carried along" with the shockwave for a certain period of time, until they eventually settle into a new equilibrium state. This behavior can also be seen in other shockwave spacetimes, such as the ones discussed in the Dray-'tHooft paper.

To answer your second question, the treatment of boundary conditions for electric fields (or other types of matter) across a shockwave is a topic that is still being studied and researched. As you mentioned, there is no mention of any special boundary conditions in the paper you referenced. This is because the assumption is that the matter fields will behave smoothly across the shockwave, as the shockwave only affects the metric and not the matter fields themselves. However, there have been some recent studies that suggest that there may be some non-trivial behavior at the boundary, especially in the case of charged matter. Further research is needed to fully understand the boundary conditions for matter fields in shockwave spacetimes.

I hope this helps answer your questions and provides some insight into the behavior of electric fields in gravitational shockwave geometries. Thank you for your interest in this topic and happy researching!